Table of contents
- 0. Review of Algebra(0)
- 1. Equations & Inequalities(0)
- 2. Graphs of Equations(0)
- 3. Functions(0)
- 4. Polynomial Functions(0)
- 5. Rational Functions(0)
- 6. Exponential & Logarithmic Functions(0)
- 7. Systems of Equations & Matrices(0)
- 8. Conic Sections(0)
- 9. Sequences, Series, & Induction(0)
- 10. Combinatorics & Probability(0)
9. Sequences, Series, & Induction
Sequences
9. Sequences, Series, & Induction
Sequences: Study with Video Lessons, Practice Problems & Examples
65PRACTICE PROBLEM
Prove that the given statement is true for every positive integer n. Use mathematical induction.
![sum from i equals 1 to n of 3 times 4 to the power of i equals 4 open parentheses 4 to the power of n minus 1 close parentheses {"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mn>3</mn><mo>·</mo><msup><mn>4</mn><mi>i</mi></msup><mo>=</mo><mn>4</mn><mfenced><mrow><msup><mn>4</mn><mi>n</mi></msup><mo>-</mo><mn>1</mn></mrow></mfenced></mstyle></math>","truncated":false}](https://lightcat-files.s3.amazonaws.com/problem_images/202ab8e57f03948e-1671631860664.jpg)
Prove that the given statement is true for every positive integer n. Use mathematical induction.