已知数列{an}满足a1=1,an=2a下标(n-1)+2^n(n≥2,n∈N*) (1)求证数列{an/2^n}是等差数列(2)记bn={an/2^n},求{bn}前n项和Sn不好意思,是a1=2.
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![已知数列{an}满足a1=1,an=2a下标(n-1)+2^n(n≥2,n∈N*) (1)求证数列{an/2^n}是等差数列(2)记bn={an/2^n},求{bn}前n项和Sn不好意思,是a1=2.](/uploads/image/z/9490330-10-0.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ban%7D%E6%BB%A1%E8%B6%B3a1%3D1%2Can%3D2a%E4%B8%8B%E6%A0%87%EF%BC%88n-1%EF%BC%89%2B2%5En%EF%BC%88n%E2%89%A52%2Cn%E2%88%88N%2A%EF%BC%89+%EF%BC%881%EF%BC%89%E6%B1%82%E8%AF%81%E6%95%B0%E5%88%97%7Ban%2F2%5En%7D%E6%98%AF%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%EF%BC%882%EF%BC%89%E8%AE%B0bn%3D%7Ban%2F2%5En%7D%2C%E6%B1%82%7Bbn%7D%E5%89%8Dn%E9%A1%B9%E5%92%8CSn%E4%B8%8D%E5%A5%BD%E6%84%8F%E6%80%9D%EF%BC%8C%E6%98%AFa1%3D2.)
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已知数列{an}满足a1=1,an=2a下标(n-1)+2^n(n≥2,n∈N*) (1)求证数列{an/2^n}是等差数列(2)记bn={an/2^n},求{bn}前n项和Sn不好意思,是a1=2.
已知数列{an}满足a1=1,an=2a下标(n-1)+2^n(n≥2,n∈N*) (1)求证数列{an/2^n}是等差数列
(2)记bn={an/2^n},求{bn}前n项和Sn
不好意思,是a1=2.
已知数列{an}满足a1=1,an=2a下标(n-1)+2^n(n≥2,n∈N*) (1)求证数列{an/2^n}是等差数列(2)记bn={an/2^n},求{bn}前n项和Sn不好意思,是a1=2.
an/2^n=a(n-1)/2^(n-1)+1
所以an/2^n是等差数列
b1=1
Sn=(b(1)+b(n))n/2=n(n+1)/2
原式两边除以2^n
an/2^n=a(n-1)/2^(n-1)+1
所以an/2^n是等差数列
b1=1
Sn=(b(1)+b(n))n/2=n(n+1)/2
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