已知数列an中an=1/n(n+2)试求a1+a2+a3+……+an……的值

问题描述:

已知数列an中an=1/n(n+2)试求a1+a2+a3+……+an……的值

an=1/n(n+2)=1/2[1/n-1/(n+2)]
a1+a2+...+an
=1/2[1-1/3]+1/2[1/2-1/4]+.+1/2[1/n-1/(n+2)]
=1/2[1+1/2-1/(n+1)-1/(n+2)]
=3/4-1/2*(2n+3)/[(n+1)(n+2)]