7. Prove that for every x E (-1,1)11– 2x + 3x² – 4x° + ... =E(-1)" (n + 1)x"--(1+x)²°n=0Make sure you justify the uniform convergences if you use limit theorems.Hint: Use the differentiation of the uniform limit theorem.

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Answered: 7. Prove that for every x E (-1,1) 1 1–…

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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7. Prove that for every x E (-1,1) 1 1– 2x + 3x2 – 4x³ E(-1)" (n + 1)x" : - (1+x)² ` n=0 Make sure you justify the uniform convergences if you use limit theorems. Hint: Use the differentiation of the uniform limit theorem.