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# Proof by induction watch

1. Prove that for all integers n≥1,
1+2+2²+...+2^n=2^(n-1)-1, by induction.

I encountered this question in my studies and I couldn't find an integer value for n that would make the equation true. So would you guys help me? Thanks for your help.
2. Actually the sum should be .
It's easy to directly check this as the series is just a geometric series.
3. (Original post by B_9710)
Actually the sum should be .
It's easy to directly check this as the series is just a geometric series.
That's true. I made a mistake the sum is actually 2^{n+1}-1

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