数列1/2,3/4,7/8,2的n次方-1/2的n次方...的前n项和sn=

问题描述:

数列1/2,3/4,7/8,2的n次方-1/2的n次方...的前n项和sn=

不难,1/2=1-1/2,3/4=1-1/4=1-1/2*2,7/8=1-1/2*3,2*n-1/2*n=1-1/2*n
sn=(1+1+1+...+1)-(1/2+1/2*2+1/2*3+...+1/2*n)
=n-【1/2(1-1/2*n)】/(1/2)
=n-(1-1/2*n)