已知数列{an}的前几项的和为sn ,且a1=0.5,an=-2SnSn-1证明数列{1/Sn}为等差数列
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已知数列{an}的前几项的和为sn ,且a1=0.5,an=-2SnSn-1证明数列{1/Sn}为等差数列
![已知数列{an}的前几项的和为sn ,且a1=0.5,an=-2SnSn-1证明数列{1/Sn}为等差数列](/uploads/image/z/2238937-25-7.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8D%E5%87%A0%E9%A1%B9%E7%9A%84%E5%92%8C%E4%B8%BAsn+%2C%E4%B8%94a1%3D0.5%2Can%3D-2SnSn-1%E8%AF%81%E6%98%8E%E6%95%B0%E5%88%97%7B1%2FSn%7D%E4%B8%BA%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97)
∵Sn-Sn-1=-an
Sn-Sn-1=-an/2
∴d=1/Sn-1/Sn-1=(Sn-Sn-1)/SnSn-1=2
1/S1=1/a1=2
∴{1/Sn}为首项=2,公差=2的等差数列
Sn-Sn-1=-an/2
∴d=1/Sn-1/Sn-1=(Sn-Sn-1)/SnSn-1=2
1/S1=1/a1=2
∴{1/Sn}为首项=2,公差=2的等差数列
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