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Prove that for n=1, 2, 3... [(n+1)/2]+[...

Prove that for `n=1, 2, 3...` `[(n+1)/2]+[(n+2)/4]+[(n+4)/8]+[(n+8)/16]+...=n` where `[x]` represents Greatest Integer Function

A

`n- 1`

B

n

C

`n+2`

D

2n

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