manganellicaitl
manganellicaitl
24-05-2017
Mathematics
contestada
s12 for the series 1+2+4+8+
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LammettHash
LammettHash
24-05-2017
[tex]S_{12}=1+2+4+8+\cdots+2048[/tex]
[tex]S_{12}=2^0+2^1+\cdots+2^{11}[/tex]
[tex]2S_{12}=2^1+2^2+\cdots+2^{12}[/tex]
[tex]\implies S_{12}-2S_{12}=2^0-2^{12}[/tex]
[tex]-S_{12}=1-2^{12}[/tex]
[tex]S_{12}=2^{12}-1[/tex]
[tex]S_{12}=4096-1=4095[/tex]
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