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Single Variable Calculus

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Moderate

Using Taylor Series to Evaluate a Numerical Series II

SVCALC-CZ1LJE

Use the Taylor series for $\tan^{-1}x$ at $x=0$ to find the sum of the series:

$$1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\ldots$$

A

$\cfrac{\pi}{6}$

B

$\cfrac{\pi}{4}$

C

$\cfrac{\pi}{3}$

D

$\cfrac{\pi}{2}$

E

$\pi$