数列a数列b,满足ab=1,且a=n²+3n+2,则数列b的前10项和为?
问题描述：
数列a数列b,满足ab=1,且a=n²+3n+2,则数列b的前10项和为?
A.1/3
B.5/12
C.1/2
D.7/12
答
ab=1a=n²+3n+2b=1/(n²+3n+2)b=1/[(n+2)(n+1)]b=1/(n+1) - 1/(n+2)b1加到b10=1/2-1/3+1/3-1/4+...+1/11 - 1/12 =1/2-1/12 =5/12