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10-05-2017
Mathematics

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

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LammettHash LammettHash

10-05-2017

[tex]S=1+2+4+\cdots+1024+2048=1+2^1+2^2+\cdots+2^{10}+2^{11}[/tex]
[tex]2S=2^1+2^2+2^3+\cdots+2^{11}+2^{12}[/tex]
[tex]\implies S-2S=1-2^{12}[/tex]
[tex]\implies -S=1-4096[/tex]
[tex]\implies S=4095[/tex]

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