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数学
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已知数列{an}中,a1=1,前n项和Sn满足Sn√(Sn-1)-S(n-1)√Sn=2√[SnS(n-1)],则an=?
人气:305 ℃ 时间:2020-06-20 16:52:12
解答
Sn√(Sn-1)-S(n-1)√Sn=2√[SnS(n-1)]===>√[SnS(n-1)][√[Sn - √S(n-1)] =2√[SnS(n-1)]===>
√[Sn - √S(n-1) = 2 用n=2,……n构造出n - 1个像前面一样等式并相加得 :
√Sn - √S1 = 2(n - 1)
sn =(2n - 1 )^2
an = sn - s(n-1) =12n - 15 (n >=2)
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