Question Number 104940 by 175mohamed last updated on 24/Jul/20

Commented bybramlex last updated on 25/Jul/20

Σ_(i=0) ^∞ ⌊ ((n+2^i )/2^(i+1) )⌋   n=1 , ⌊((1+1)/2)⌋+⌊((1+2)/4)⌋+...= 1  n=2 , ⌊((2+1)/2)⌋+⌊((2+2)/4)⌋+...=2  n=3, ⌊((3+1)/2)⌋+⌊((3+2)/4)⌋+...=3  n=4 ,⌊((4+1)/2)⌋+⌊((4+2)/4)⌋+⌊((4+3)/8)⌋+...=4  Σ_(i=0) ^∞ ⌊((n+2^i )/2^(i+1) )⌋ = n , ∀n ∈N

Answered by Ar Brandon last updated on 25/Jul/20

A_i =Σ_(i=0) ^∞ [((n+2^i )/2^(i+1) )]=Σ_(i=0) ^∞ {(n/2^(i+1) )+(1/2)}       =(n/2)Σ_(i=0) ^∞ (1/2^i )+Σ_(i=0) ^∞ (1/2)

Commented bymathmax by abdo last updated on 25/Jul/20

no sir  [...] mean integr parts(floor) you answer another question..!

Commented byAr Brandon last updated on 25/Jul/20

Oh ! OK Thanks