9. Sequences, Series, & Induction

Sequences

9. Sequences, Series, & Induction

Sequences

Guided videos.

Learn with Patrick

Go to the course

Guided course

8:22

Introduction to Sequences

Writing a General Formula

Showing 5 of 5 videos

Learn with other creators

Finding Terms in a Sequence Given the General Term

01:51

Finding Terms in a Sequence Given the General Term

Writing The First Four Terms of a Sequence

The Organic Chemistry Tutor

449

views

Practice this topic

Multiple Choice

The first 4 terms of a sequence are $\left\lbrace\sqrt3,2\sqrt3,3\sqrt3,4\sqrt3,\ldots\right\rbrace$ . Continuing this pattern, find the $7^{\th}$ term.

149

views

Multiple Choice

Determine the first 3 terms of the sequence given by the general formula

$a_{n}=\frac{1}{n!+1}$

Write the first 6 terms of the sequence given by the recursive formula $a_{n}=a_{n-2}+a_{n-1}$ ; $a_1=1$ ; $a_2=1$ .

129

views

Practice

tdx-single - c3501d1f

views

Practice

tdx-single - 696e25af

views

Practice

tdx-single - fe3c2259

views

Practice

tdx-single - fd2722fd

views

Practice

tdx-single - 5ab62a8b

views

Practice

tdx-single - 8738d3fc

views

Practice

tdx-single - 1c0f4e7f

views

Practice

tdx-single - bfa2eb20

views

Practice

tdx-single - 140fc766

views

Textbook Question

In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=3n+2

210

views

Textbook Question

In Exercises 1–6, write the first four terms of each sequence whose general term is given. a_n = 7n - 4

331

views

Textbook Question

In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=3^n

300

views

Textbook Question

In Exercises 1–6, write the first four terms of each sequence whose general term is given. a_n = 1/(n - 1)!

256

views

Textbook Question

In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=(−3)^n

235

views

Textbook Question

Evaluate 40!/(4! 38!)

266

views

Textbook Question

In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=(−1)^n(n+3)

226

views

Textbook Question

In Exercises 8–9, find each indicated sum. This is a summation, refer to the textbook.

207

views

Textbook Question

In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=2n/(n+4)

212

views

Textbook Question

In Exercises 10–11, express each sum using summation notation. Use i for the index of summation. 1/3 + 2/4 + 3/5 + ... + 15/17

249

views

Textbook Question

In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=(−1)^n+1/(2^n−1)

207

views

Textbook Question

The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a_1=7 and a_n=a_n-1 + 5 for n≥2

217

views

Textbook Question

The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a_1=3 and a_n=4a_n-1 for n≥2

228

views

Textbook Question

The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a_1=4 and a_n=2a_n-1 + 3 for n≥2

265

views

Textbook Question

In Exercises 19–22, the general term of a sequence is given and involves a factorial. Write the first four terms of each sequence. a_n = n^2/n!

297

views

Textbook Question

In Exercises 19–22, the general term of a sequence is given and involves a factorial. Write the first four terms of each sequence. a_n=2(n+1)!

213

views

Textbook Question

In Exercises 23–28, evaluate each factorial expression. 17!/15!

269

views

Textbook Question

In Exercises 23–28, evaluate each factorial expression. 16!/2!14!

239

views

Textbook Question

In Exercises 23–28, evaluate each factorial expression. (n+2)!/n!

254

views

Textbook Question

In Exercises 29–42, find each indicated sum. 6Σi=1 5i

245

views

Textbook Question

In Exercises 29–42, find each indicated sum. 4Σi=1 2i^2

210

views

Textbook Question

In Exercises 29–42, find each indicated sum. 5Σk=1 k(k+4)

237

views

Textbook Question

In Exercises 29–42, find each indicated sum. 4Σi=1 (−1/2)^i

191

views

Textbook Question

In Exercises 29–42, find each indicated sum. 9Σi=5 11

194

views

Textbook Question

In Exercises 29–42, find each indicated sum. 4Σi=0 (−1)^i/i!

247

views

Textbook Question

In Exercises 29–42, find each indicated sum. 5Σi=1 i!/(i−1)!

219

views

Textbook Question

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1^2+2^2+3^2+⋯+ 15^2

228

views

Textbook Question

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 2+2^2+2^3+⋯+ 2^11

304

views

Textbook Question

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1+2+3+⋯+ 30

286

views

Textbook Question

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1/2+2/3+3/4+⋯+ 14/(14+1)

221

views

Textbook Question

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 4+4^2/2+4^3/3+⋯+ 4^n/n

274

views

Textbook Question

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1+3+5+⋯+ (2n−1)

276

views

Textbook Question

In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. 5+7+9+11+⋯+ 31

702

views

Textbook Question

In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. a+ar+ar2+⋯+ ar^12

209

views

Textbook Question

In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. a+(a+d)+(a+2d)+⋯+ (a+nd)

290

views

Textbook Question

In Exercises 61–68, use the graphs of and to find each indicated sum.

In Exercises 61–68, use the graphs of and to find each indicated sum.

In Exercises 61–68, use the graphs of and to find each indicated sum.

In Exercises 61–68, use the graphs of and to find each indicated sum.

In Exercises 61–68, use the graphs of and to find each indicated sum.

In Exercises 61–68, use the graphs of and to find each indicated sum.

5Σi=1 a_i^2+5Σi=1 b_i^2

204

views

Textbook Question

In Exercises 61–68, use the graphs of and to find each indicated sum.

5Σi=1 a_i^2−5Σi=3 b_i^2

190

views

Textbook Question

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 200!/198!

226

views

Textbook Question

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. (300/20)!

259

views

Textbook Question

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 20!/300

244

views

Textbook Question

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 20!/(20−3)!

198

views

Textbook Question

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 54!/(54−3)!3!

235

views

Textbook Question

Write the first five terms of the sequence whose first term is 9 and whose general term is an= (an−1)/2 if a_n-1 is even, a_n=3a_n-1 + 5 if a_n-1 is odd for n≥2.

224

views

Textbook Question

In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n. 2 + 4 + 8 + ... + 2^n = 2^(n+1) - 2

142

views

Textbook Question

In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n. 1 + 2 + 2^2 + ... + 2^(n-1) = 2^n - 1

111

views

Textbook Question

In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n. 3 + 7 + 11 + ... + (4n - 1) = n(2n + 1)

views

Textbook Question

In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n. 1 + 3 + 5 + ... + (2n - 1) = n^2

views

Textbook Question

In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n. 4 + 8 + 12 + ... + 4n = 2n(n + 1)

views

Textbook Question

In Exercises 5–10, a statement Sn about the positive integers is given. Write statements S_k and S_(k+1) simplifying statement S_(k+1) completely. Sn: 2 is a factor of n^2 - n + 2.

views

Textbook Question

In Exercises 5–10, a statement Sn about the positive integers is given. Write statements S_k and S_(k+1) simplifying statement S_(k+1) completely. Sn: 4 + 8 + 12 + ... + 4n = 2n(n + 1)

views

Textbook Question

In Exercises 1–4, a statement S_n about the positive integers is given. Write statements S1, S2 and S3 and show that each of these statements is true. Sn: 3 is a factor of n^3 - n.

views

Textbook Question

In Exercises 1–4, a statement S_n about the positive integers is given. Write statements S1, S2 and S3 and show that each of these statements is true. Sn: 3 + 4 + 5 + ... + (n + 2) = n(n + 5)/2

views

Textbook Question

In Exercises 1–4, a statement S_n about the positive integers is given. Write statements S1, S2 and S3 and show that each of these statements is true. Sn: 1 + 3 + 5 + ... + (2n - 1) = n^2

views

Textbook Question

In Exercises 25–34, use mathematical induction to prove that each statement is true for every positive integer n. 6 is a factor of n(n + 1)(n + 2).

113

views

Textbook Question

In Exercises 25–34, use mathematical induction to prove that each statement is true for every positive integer n. 2 is a factor of n^2 - n.

views

Textbook Question

In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n. 1/(1 · 2) + 1/(2 · 3) + 1/(3 · 4) + ... + 1/(n(n+1)) = n/(n + 1)

views

Textbook Question

In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n. 1 · 2 + 2 · 3 + 3 · 4 + ... + n(n + 1) = n(n + 1)(n + 2)/3

views

Textbook Question

In Exercises 25–34, use mathematical induction to prove that each statement is true for every positive integer n. (ab)^n = a^n b^n

165

views

Textbook Question

In Exercises 25–34, use mathematical induction to prove that each statement is true for every positive integer n. n + 2 > n

views

Textbook Question

In Exercises 25–34, use mathematical induction to prove that each statement is true for every positive integer n. n Σ (i = 1) 5 · 6^i = 6(6^n - 1)

views

Textbook Question

Use mathematical induction to prove that the statement is true for every positive integer n. 1 + 4 + 4^2 + ... + 4^(n-1) = ((4^n)-1)/3

views

Textbook Question

Use mathematical induction to prove that the statement is true for every positive integer n. 5 + 10 + 15 + ... + 5n = (5n(n+1))/2

273

views

Textbook Question

In Exercises 5–10, a statement Sn about the positive integers is given. Write statements S_k and S_(k+1) simplifying statement S_(k+1) completely. Sn: 3 + 7 + 11 + ... + (4n - 1) = n(2n + 1)

views

Showing 80 of 80 practice

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing

9. Sequences, Series, & Induction

Sequences

Learn with Patrick

Learn with other creators

Practice this topic