已知数列a0,a1,a2,…,an,…满足关系式(3-an+1)(6+an)=18,且a0=3,则ni=01ai的值是______.-数学

题目简介

已知数列a0,a1,a2,…,an,…满足关系式(3-an+1)(6+an)=18,且a0=3,则ni=01ai的值是______.-数学

题目详情

已知数列a0,a1,a2,…,an,…满足关系式(3-an+1)(6+an)=18,且a0=3,则
n


i=0
1
ai
的值是______.
题型:填空题难度:中档来源:不详

答案

class="stub"1
an+1
=class="stub"2
an
+class="stub"1
3

令bn=class="stub"1
an
+class="stub"1
3
,得b0=class="stub"2
3
,bn=2bn-1,
∴bn=class="stub"2
3
×2n.
class="stub"1
an
=
2n+1-1
3


n


i-0
class="stub"1
ai
=class="stub"1
3
(22+23+…+2n+1)-class="stub"1
3
×n

=class="stub"1
3
×
4(1-2n)
1-2
-class="stub"n
3

=class="stub"1
3
(2n+2-n-4)

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