Provide an appropriate response.
-Let $\mathrm { s } _ { \mathrm { k } }$ denote the kth partial sum of the alternating harmonic series. Compute $\mathrm { s } 17 , \mathrm {~s} 18$, and $\frac { \mathrm { s } 17 + \mathrm { s } 18 } { 2 }$. Which of these is closest to the exact sum ( $\ln 2$ ) of the alternating harmonic series?
A) 518
B) $\frac { s 17 ^ { + s } 18 } { 2 }$
C) $s 17$

Question

Quizplus · Accepted Answer

The alternating harmonic series converges to $\ln(2)$, and the average of two consecutive partial sums provides a better approximation to the sum than either of the individual partial sums. This is because the series alternates and converges, so averaging two terms reduces the error from the alternating signs.

Provide an Appropriate Response sk\mathrm { s } _ { \mathrm { k } }sk​

Provide an Appropriate Response $\mathrm { s } _ { \mathrm { k } }$