设数列1/(1+根2),1/(根2+根3),……,1/(根n+根(n+1))的前n项和为Sn,求Sn

问题描述:

设数列1/(1+根2),1/(根2+根3),……,1/(根n+根(n+1))的前n项和为Sn,求Sn

an=1/(√n+√n+1)=√(n+1)-√n
故Sn=a1+a2+……+an
=√2-√1+√3-√2+……+√(n+1)-√n
=√(n+1)-1