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son4ous [18]
2 years ago
12

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

Mathematics
1 answer:
Tatiana [17]2 years ago
5 0
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 kth 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.
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