问题
填空题
{an}是无穷数列,已知an是二项式(1+2x)n(n∈N*)的展开式各项系数的和,记Pn=
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答案
由题意可得an=3n,∴Pn=
+1 a1
+…+1 a2
=1 an
+1 3
+1 32
+…+1 33
=1 3n
=
(1-1 3
)1 3n 1- 1 3
,1- 1 3n 2
∴
Pn=lim n→∞ lim n→∞
=1- 1 3n 2
.1 2
故答案为:
.1 2