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    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.
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    Actually the sum should be  2^{n+1}-1 .
    It's easy to directly check this as the series is just a geometric series.
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    (Original post by B_9710)
    Actually the sum should be  2^{n+1}-1 .
    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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Updated: October 31, 2016
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