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.1/3B.5/12C.1/2D.7/12
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
B
答
B
b=1/a=1/(n+1)(n+2)=1/(n+1) - 1/(n+2)
b1=1/2 - 1/3
b2=1/3 - 1/4
......
b10=1/11 - 1/12
s=b1+b2+......+b10=1/2-1/12=5/12
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