Question

How to prove that $\frac{1}{\sqrt{1-x^2}}=\sum _{n=0}^{\infty }\frac{(2n)!}{4^n(n!)^2}x^{2n}$?

score 76 · Answer 1 · 2019-11-10 01:16:44

76

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284

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score 775 · Answer 7 · 2019-11-11 16:28:36

775

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score 21 · Answer 8 · 2019-11-11 16:35:30

21

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score 35 · Answer 10 · 2019-11-12 21:00:12

35

Views

Differentiability and Taylor series of $\sum_{k=0}^{\infty} \frac{1}{k ! \cdot\left(1+4^{k} x^{2}\right)}$.

Published on 12 Nov 2019 - 21:00

score 408 · Answer 11 · 2019-11-12 23:57:43

408

Views

What does Taylor series have to do with this problem?

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score 54 · Answer 12 · 2019-11-13 01:32:28

54

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score 1.9k · Answer 13 · 2019-11-14 09:19:33

1.9k

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56

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score 565 · Answer 15 · 2019-11-14 17:17:13

565

Views

How do I find the Taylor series of f(x) = 5cos(x), a = 11pi????

Published on 14 Nov 2019 - 17:17

List Question

How to prove that $\frac{1}{\sqrt{1-x^2}}=\sum _{n=0}^{\infty }\frac{(2n)!}{4^n(n!)^2}x^{2n}$?

Is the assumption consider cheating in mathematics?

Taylor Expansion of Matrices?

Taylor's Inequality: defining an interval

Why do we use Taylor series for estimations?

Taylor Inequality: Plugging in any x to find n

Taylor series: Assuming the x-value for which there is maximum magnitude of 6th derivative?

Using Taylor expansion to prove equality involving central difference operator

How to expand $b\int_0^\infty \operatorname{sech}^2\big(b\cdot f(x)\big)\,dx$ for large $b$?

Differentiability and Taylor series of $\sum_{k=0}^{\infty} \frac{1}{k ! \cdot\left(1+4^{k} x^{2}\right)}$.

What does Taylor series have to do with this problem?

Taylor expansion of $\ln(1+\frac{x}{n})$

Doubt about Taylor series: do successive derivatives on a point determine the whole function?

Calculus, Pattern

How do I find the Taylor series of f(x) = 5cos(x), a = 11pi????

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