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设等比数列{an}的前n项的和为Sn,前n项的倒数之和为Tn,则Sn/Tn=
人气:263 ℃ 时间:2020-01-28 19:20:04
解答
设等比数列{an}的公比为q
侧:S n=a1(q的n次方-1)/(q-1)
Tn=1/a1+1/a2+,=1/a1[((1/q)的n次方-1)/(1/q-1)
= [(q的n次方-1)/(q-1)]/[ a1• q的(n-1`)次方]
=[(q的n次方-1)/(q-1)]/(an)
故:Sn/Tn=a1•an
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