We investigate the convergence of the binomial series By Exercise 94, T a (x) converges for |x|

Question:

We investigate the convergence of the binomial series

Ta(x) = M8 n=0

By Exercise 94, T_a(x) converges for |x| a(x) = (1 + x)^a.

(a) Verify the identity a a(a) = n(a) + (n + )( + 1) 1) n+1 (b) Use (a) to show that y = Ta(x) satisfies

Data From Exercise 94

We investigate the convergence of the binomial series

Ta(x) = M8 n=0

Prove that T_a(x) has radius of convergence R = 1 if a is not a whole number. What is the radius of convergence if a is a whole number?

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Dec 19, 2023 06:28 AM

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We investigate the convergence of the binomial series By Exercise 94, T a (x) converges for |x|

Question:

Ta(x) = M8 Σ n=0

Step by Step Answer:

a a D n a n 1 n n n1 Thus c Moreover b Differentiating ...View the full answer

Calculus

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