数列{an} ,{bn}满足anbn = 1,an = n2 + 3n + 2,则{bn}的前十项的和为

题目

数列{an} ,{bn}满足anbn = 1,an = n2 + 3n + 2,则{bn}的前十项的和为

答案

bn=1/( n2 + 3n + 2)
=1/((n+1)(n+2))
S10=1/(2*3)+1/(3*4).+1/(11*12)
=1/2-1/3+1/3-.+1/11-1/12
=1/2-1/12
=5/12