The title explains the problem fairly well; is there a way to prove by induction that ∑∞n=112n=1. If not are there other ways?
I have thought of showing it by rewriting the series so that. ∞∑n=112n=1⟹∞∑n=112(12)n−1=1
And then from there conclude that it is a geometric series with the values r=1/2 and a=1/2 thus ∞∑n=112n=1/21−1/2=1
This seems like kind of a vodoo proof, so i was wondering if its possible to do this by induction?
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