By the error estimation theorem for convergent alternating series, the upper estimate to the error in approximating the sum of $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { \sqrt { n } }$ using the first three terms is

A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 1 } { 8 }$
D) $\frac { 1 } { 16 }$
E) $\frac { 1 } { 32 }$

Question

By the error estimation theorem for convergent alternating series, the upper estimate to the error in approximating the sum of

\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { \sqrt { n } }

using the first three terms is

A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 1 } { 8 }$
D) $\frac { 1 } { 16 }$
E) $\frac { 1 } { 32 }$

Quizplus · Accepted Answer

The error estimation theorem for convergent alternating series states that the error is less than or equal to the absolute value of the first omitted term. Here, the fourth term is $\frac{1}{\sqrt{4}} = \frac{1}{2}$.

By the Error Estimation Theorem for Convergent Alternating Series, the Upper