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Prove that [x]=[x/2]+[(x+1)/2] where [.]...

Prove that `[x]=[x/2]+[(x+1)/2]` where [.] denote greatest integer function and n be any positive integer than show that
`[(n+1)/2]+[(n+2)/4]+[(n+4)/8]+[(n+8)/16]+…..=n`

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