Express the series in summation notation where the sums are to n terms. 1-3 + 9-27 +...
you cannot sum n from 1 to n
You need a dummy index, such as k. So use
n
∑ (-1)^(k+1) * 3^k
k=1
The series can be expressed in summation notation as follows:
∑ (-1)^(n+1) * 3^n
Where the summation runs from n=1 to n. The exponent on 3 increases by 1 in each term, and the (-1)^(n+1) factor alternates between positive and negative to give the series its alternating sign.