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.