Sunday, 2 March 2014

sequences and series - Prove by induction that sumin=1nftyfrac12n=1

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=1n=112(12)n1=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=1/211/2=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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