Ok, so I'm not very good with these proving by induction thingies. Need a little help please.
How do I prove
$$\sum_{j=0}^n\left(-\frac12\right)^j=\frac{2^{n+1}+(-1)^n}{3\cdot2^n}$$
when $n$ is a non-negative integer.
I got the basis step and such down, but I'm pretty bad with exponents so I am having a difficult time in the induction step.
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