已知数列{an}满足a1=1,a[n+1]=2a[n]+1(n∈N) 证明:n/2-1/3
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已知数列{an}满足a1=1,a[n+1]=2a[n]+1(n∈N)证明:n/2-1/3已知数列{an}满足a1=1,a[n+1]=2a[n]+1(n∈N)证明:n/2-1/3已知数列{an}满足a1
已知数列{an}满足a1=1,a[n+1]=2a[n]+1(n∈N) 证明:n/2-1/3
已知数列{an}满足a1=1,a[n+1]=2a[n]+1(n∈N) 证明:n/2-1/3
已知数列{an}满足a1=1,a[n+1]=2a[n]+1(n∈N) 证明:n/2-1/3
解
a[n+1]=2a[n]+1,a[n+1]+1=2(a[n]+1)
所以{a[n]+1}是以1+1=2为首项,公比2的等比数列
a[n]=2^n-1
a[n-1]/a[n]=1/2-1/2(2^n-1)
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