Question

Rewrite the sum 1/2-1/4+1/8-1/16+1/32-1/64+1/128 using sigma notation

Answer 1

start with
\[\sum_{k=1}^7\frac{1}{2^k}\] and then make it alternate sign

Answer 2

gimmick there is to write
\[(-1)^k\] or
\[(-1)^{k+1}\] depending on which terms are positive and which are negative in this case you will want
\[\sum_{k=1}^7\frac{(-1)^{k+1}}{2^k}\]