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数学
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等比数列题 已知等比数列an前n项和为Sn=(1/3)的n次方+a,a的值为多少?
人气:174 ℃ 时间:2019-08-19 05:30:45
解答
由等比数列求和公式
s(n)=a(1)(q^n-1)/(q-1)
得a(1)(q^n-1)/(q-1)=3^n+a
化简得
a(1)q^n-a(1)=(q-1)3^n+a(q-1)
左右两边对应可得
q=3 a(1)=q-1=2 a(q-1)=-a(1)
2a=-2即a=-1
注意:上面“^”表示乘方.“3^n”即三的n次方.
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