s/2= 1/4+2/8+……+(n- 1)/2^n+n/2^(n+ 1)

These two types need to be reduced:

s/2= 1/2+ 1/4+ 1/8+……+ 1/2^n-n/2^(n+ 1)

= 1/2*( 1-( 1/2)^n)÷( 1- 1/2)-n/2^(n+ 1)

= 1- 1/2^n-n/2^(n+ 1)

∴s=2- 1/2^(n- 1)-n/2^n

So the limit of sum is 2. Forget the translation, I can't.