Find the sum of each finite geometric series. 1 + 2 + 4 + … + 2048

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asked Oct 24, 2018 151k views

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Find the sum of each finite geometric series. 1 + 2 + 4 + … + 2048

Mathematics
high-school

Bruno Habermann asked

by Bruno Habermann

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$S=1+2+4+\cdots+1024+2048=1+2^1+2^2+\cdots+2^(10)+2^(11)$

$2S=2^1+2^2+2^3+\cdots+2^(11)+2^(12)$

$\implies S-2S=1-2^(12)$

$\implies -S=1-4096$

$\implies S=4095$

Bugfish answered Oct 28, 2018

by Bugfish

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