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Finding the Error for an Alternating Series

APCALC-BBVUEA

Find the error when approximating:

$$\sum _{ n=1 }^{ \infty }{ ( -1 ) ^{ n+1 }\cfrac { 1 }{ n } } $$

...using the first four terms.

A

$\cfrac{7}{12}$

B

$\cfrac{5}{12}$

C

$\cfrac{1}{5}$

D

$\cfrac{1}{4}$