Question

数列{a n }、{b n }满足a n •b n =1，a n =n 2 +3n+2，则{b n }的前10项之和等于

Answer 1

∵a _n•b _n=1

∴b _n=

1

n 2 +3n+2 =

1

(n+1)(n+2)

∴s10=

1

2×3 +

1

3×4 ++

1

10×11 +

1

11×12 =（

1

2 -

1

3 ）+ (

1

3 -

1

4 ) ++(

1

10 -

1

11 ) +(

1

11 -

1

12 ) =

1

2 -

1

12 =

5

12

故选项为B．