数列{an},{bn}满足an*bn=1,an=n^2+3n+2,则{bn}的前10项和为多少

问题描述:

数列{an},{bn}满足an*bn=1,an=n^2+3n+2,则{bn}的前10项和为多少

bn=1/(n+1)(n+2)=1/(n+1)-1/(n+2)
所以b1+b2+……+b10=(1/2-1/3)+(1/3-1/4)+……+(1/11-1/12)
=1/2-1/12=5/12