Single Variable Calculus

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Moderate

Summing a Rearrangement of a Conditionally Convergent Series

SVCALC-LZJ8JD

It is a fact that the alternating harmonic series:

$$1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\ldots$$

...converges to $\ln2$. Use this fact to find the sum of the series:

$$1-\frac{1}{2}-\frac{1}{4}+\frac{1}{3}-\frac{1}{6}-\frac{1}{8}+\ldots$$

(Hint: combine each positive term with the one following it.)

A

$-\cfrac{1}{2}\ln 2$

B

$-\cfrac{1}{3}\ln 2$

C

$0$

D

$\cfrac{1}{3}\ln 2$

E

$\cfrac{1}{2}\ln 2$

F

$\ln 2$