Question

bn=

1

n2+3n+2

，則{b_n}的前10項(xiàng)之和為（　�。�

• A．

  1

  3

• B．

  5

  12

• C．

  1

  2

• D．

  7

  12

Answer 1

分析：利用裂項(xiàng)法可得b_n=

1

(n+1)(n+2)

=

1

n+1

-

1

n+2

，從而可求{b_n}的前10項(xiàng)之和．

解答：解：∵b_n=

1

(n+1)(n+2)

=

1

n+1

-

1

n+2

，
∴b₁+b₂+…+b₁₀
=（

1

2

-

1

3

）+（

1

3

-

1

4

）+…+（

1

11

-

1

12

）
=

1

2

-

1

12

=

5

12

．
故選B．

點(diǎn)評(píng)：本題考查數(shù)列的求和，突出考查裂項(xiàng)法的應(yīng)用，屬于中檔題．