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Let In = | (1– t²)" dt, for any nonnegative integer n. 1°) Prove that, for any positive integer n, (2n + 1) I, = 2n I,-1- 2°) Deduce that, for any positive integer n, 2" . n! In 3.5. 7.. (2n +1)*

Let In = | (1– t²)" dt, for any nonnegative integer n. 1°) Prove that, for any positive integer n, (2n + 1) I, = 2n I,-1- 2°) Deduce that, for any positive integer n, 2" . n! In 3.5. 7.. (2n +1)*

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let In = | (1 – t²)" dt, for any nonnegative integer n. 1°) Prove that, for any positive integer n, (2n + 1) I, = 2n I,-1. 2°) Deduce that, for any positive integer n, 2" . n! 3.5. 7.. (2n +1)* In
Transcribed Image Text:Let In = | (1 – t²)" dt, for any nonnegative integer n. 1°) Prove that, for any positive integer n, (2n + 1) I, = 2n I,-1. 2°) Deduce that, for any positive integer n, 2" . n! 3.5. 7.. (2n +1)* In
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