数列{an},{bn}的通项公式满足:an•bn=1,且an=n2+3n+2,则数列{bn}的前10项之和是______.-数学

题目简介

数列{an},{bn}的通项公式满足:an•bn=1,且an=n2+3n+2,则数列{bn}的前10项之和是______.-数学

题目详情

数列{an},{bn}的通项公式满足:an•bn=1,且an=n2+3n+2,则数列{bn}的前10项之和是______.
题型:填空题难度:偏易来源:不详

答案

∵an•bn=1
∴bn=class="stub"1
n2+3n+2
=class="stub"1
(n+1)(n+2)

∴s10=class="stub"1
2×3
+class="stub"1
3×4
+   + class="stub"1
10×11
+class="stub"1
11×12
=(class="stub"1
2
-class="stub"1
3
)+(class="stub"1
3
-class="stub"1
4
) +    +(class="stub"1
10
-class="stub"1
11
) +(class="stub"1
11
-class="stub"1
12
)
=class="stub"1
2
-class="stub"1
12
=class="stub"5
12

故答案为class="stub"5
12

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