Question

S12 for the series 1+2+4+8+

Answer 1

`S_(12)=1+2+4+8+\cdots+2048`

`S_(12)=2^0+2^1+\cdots+2^(11)`

`2S_(12)=2^1+2^2+\cdots+2^(12)`


`\implies S_(12)-2S_(12)=2^0-2^(12)`

`-S_(12)=1-2^(12)`

`S_(12)=2^(12)-1`

`S_(12)=4096-1=4095`