Question

Help answering this simple Series Question? I don't know what I did wrong!

Answer 1

Looks like you just evaluated the summand for the given value of $n$, whereas the question is asking you to find the value of the sum for the first $n$ terms.

Let $S_k=\displaystyle\sum_{n=1}^k\frac3{(-2)^n}$. Then $S_k$ is the $k$th partial sum.

$S_1$ happens to be the first term in the series, which is why that box is marked correct:

$S_1=\displaystyle\sum_{n=1}^1\frac3{(-2)^n}=\frac3{(-2)^1}=-1.5$

But the next partial sum is not correct:

$S_2=\displaystyle\sum_{n=1}^2\frac3{(-2)^n}=\frac3{(-2)^1}+\frac3{(-2)^2}=-0.75$

and this is not the same notion as the second term (which indeed is 0.75) in the series.