Determine how many terms should be used to estimate the sum of the entire series with an error of less than 0.001.
-$$\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } \frac { 8 } { ( n + \sqrt { n } ) ^ { 3 } }$$
A) $n \geq 18$
B) $n \geq 16$
C) $n \geq 17$
D) $\mathrm { n } \geq 15$

Question

Quizplus · Accepted Answer

The series is alternating and the error is less than the absolute value of the first omitted term. For $n \geq 16$, the term $\frac{8}{(16+\sqrt{16})^3}$ is less than 0.001.

Determine How Many Terms Should Be Used to Estimate the Sum