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

447

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.

148

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

208

views

Textbook Question

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

328

views

Textbook Question

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

299

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)!

253

views

Textbook Question

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

232

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)

224

views

Textbook Question

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

205

views

Textbook Question

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

210

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

247

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)

206

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

215

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

227

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

263

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!

295

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)!

211

views

Textbook Question

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

268

views

Textbook Question

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

238

views

Textbook Question

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

253

views

Textbook Question

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

243

views

Textbook Question

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

209

views

Textbook Question

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

236

views

Textbook Question

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

190

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!

245

views

Textbook Question

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

218

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

227

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

285

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)

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. 4+4^2/2+4^3/3+⋯+ 4^n/n

273

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)

275

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

701

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

208

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)

289

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

202

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

188

views

Textbook Question

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

225

views

Textbook Question

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

258

views

Textbook Question

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

242

views

Textbook Question

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

196

views

Textbook Question

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

234

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.

223

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

141

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

109

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).

112

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

163

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

272

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