How can I prove by induction the following statement:
$1+2+2^{2}+...+2^{n-1} =2^{n}-1; \forall n \geqslant 1$
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It's a geometric series – J. W. Tanner May 06 '20 at 16:39
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$ \frac{1-2^n}{1-2}=2^n-1 $ – Eeyore Ho May 06 '20 at 16:42
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Suggested reading: How to write a clear induction proof? – JMoravitz May 06 '20 at 16:59