Question

求S=1/2^2+2/2^3+3/2^4+4/2^5+...+n/2^(n+1)的值的解题过程

Answer 1

S=1/2^2+2/2^3+3/2^4+4/2^5+...+n/2^(n+1)

则2S=1/2+2/2^2+3/2^3+4/2^4+...+n/2^n

2式相减得:

S=2S-S

=1/2+1/2^2+2/2^3+3/2^4+...+1/2^n-n/2^(n+1)

=1/2*[1-1/2^(n+1)]/(1-1/2)-n/2^(n+1)

=4-1/2^(n-1)-n/2^(n+1)