设数列an满足:log a an+1=1+log a an,且a1+a2+…+a100=100,则a101+a102+…
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设数列an满足:log a an+1=1+log a an,且a1+a2+…+a100=100,则a101+a102+…+a200的值为
对数函数的下标太难打,附图补充说明:
![](http://img.wesiedu.com/upload/a/f1/af11bf6aae11926da5e9d3283fe08851.jpg)
![](http://img.wesiedu.com/upload/7/d7/7d7c4d9bb97a34f8f21c464904440739.jpg)
对数函数的下标太难打,附图补充说明:
![](http://img.wesiedu.com/upload/a/f1/af11bf6aae11926da5e9d3283fe08851.jpg)
![](http://img.wesiedu.com/upload/7/d7/7d7c4d9bb97a34f8f21c464904440739.jpg)
![设数列an满足:log a an+1=1+log a an,且a1+a2+…+a100=100,则a101+a102+…](/uploads/image/z/17931307-67-7.jpg?t=%E8%AE%BE%E6%95%B0%E5%88%97an%E6%BB%A1%E8%B6%B3%3Alog+a+an%2B1%3D1%2Blog+a+an%2C%E4%B8%94a1%2Ba2%2B%E2%80%A6%2Ba100%3D100%2C%E5%88%99a101%2Ba102%2B%E2%80%A6)
移项化简得 loga(an+1/an)=1
所以an+1/an=a
所以an为公比为a的等比数列
所以 a101+...+a200=a^100(a1+...+a100)=100a^100.
再问: "所以 a101+...+a200=a^100(a1+...+a100)=100a^100."这一步不明白
再答: 等比数列的性质,若公比为q,则 as=at*q^(s-t)(s>t).
对于此题,
a101=a1*a^100
a102=a2*a^100
...
a200=a100*a^100
所以an+1/an=a
所以an为公比为a的等比数列
所以 a101+...+a200=a^100(a1+...+a100)=100a^100.
再问: "所以 a101+...+a200=a^100(a1+...+a100)=100a^100."这一步不明白
再答: 等比数列的性质,若公比为q,则 as=at*q^(s-t)(s>t).
对于此题,
a101=a1*a^100
a102=a2*a^100
...
a200=a100*a^100
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