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.
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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