Sn=1/2+3/2²+5/2³+...+2n-1/2的N次方.用错位相减
问题描述：
Sn=1/2+3/2²+5/2³+...+2n-1/2的N次方.用错位相减
答
Sn=1/2+3/2²+5/2³+...+(2n-1)/2^n
1/2Sn=1/2²+3/2³+5/2^4+...+(2n-3)/2^n+(2n-1)/2^(n+1)
上式两边相减得：
1/2Sn=1/2+2/2²+2/2³+2/2^4+...+2/2^n-(2n-1)/2^(n+1)
=2(1/2+1/2²+1/2³+1/2^4+...+1/2^n)-1/2-(2n-1)/2^(n+1)
=2-2/2^n-1/2-(2n-1)/2^(n+1)
Sn =3-(2n+3)/2^n