Question

求数列{3n-1/2^n}的前n项和。（请写明过程，谢谢）

Answer 1

let
(3n-1)/2^n ≡ (An+B)/2^n - (A(n+1)+B)/2^(n+1)
=>
3n-1 ≡ 2(An+B) -(A(n+1)+B)
coef. of n =>A=3
coef. of constant
B-A=-1
B-3=-1
B=2
ie
(3n-1)/2^n ≡ (3n+2)/2^n - (3(n+1)+2)/2^(n+1)
Sn

=∑(i:1->n) (3i-1)/2^i
=∑(i:1->n) [(3i+2)/2^i - (3(i+1)+2)/2^(i+1)]
=(3+2)/2 - (3(n+1)+2)/2^(n+1)
=5/2 -(3n+5)/2^(n+1)