若等比数列an的前n项的和Sn=a-1/2^n,求实数a的值
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![若等比数列an的前n项的和Sn=a-1/2^n,求实数a的值](/uploads/image/z/5478811-43-1.jpg?t=%E8%8B%A5%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97an%E7%9A%84%E5%89%8Dn%E9%A1%B9%E7%9A%84%E5%92%8CSn%3Da-1%2F2%5En%2C%E6%B1%82%E5%AE%9E%E6%95%B0a%E7%9A%84%E5%80%BC)
若等比数列an的前n项的和Sn=a-1/2^n,求实数a的值
若等比数列an的前n项的和Sn=a-1/2^n,求实数a的值
若等比数列an的前n项的和Sn=a-1/2^n,求实数a的值
因为Sn=a-1/2^n
所以S(n-1)=a-1/2^(n-1)
两式相减得an=1/2^(n-1)-1/2^n=1/2^n
因为Sn=a-1/2^n所以S1=a-1/2^1=1/2^1
所以a=1