数列{An}满足A1=5,A2=5,A(n+1)=An+6A(n-1)(n≥2,n∈N*).若数列{A(n+1)+kAn}是等比数列已知数列{An}满足A1=5,A2=5,A(n+1)=An+6A(n-1)(n大于等于2,n属于整整数)若数列{A(n+1)+kAn}是等比数列.(1)求数列{An}的通项公式 (2)
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数列{An}满足A1=5,A2=5,A(n+1)=An+6A(n-1)(n≥2,n∈N*).若数列{A(n+1)+kAn}是等比数列已知数列{An}满足A1=5,A2=5,A(n+1)=An+6A(n-1)(n大于等于2,n属于整整数)若数列{A(n+1)+kAn}是等比数列.(1)求数列{An}的通项公式 (2)
数列{An}满足A1=5,A2=5,A(n+1)=An+6A(n-1)(n≥2,n∈N*).若数列{A(n+1)+kAn}是等比数列
已知数列{An}满足A1=5,A2=5,A(n+1)=An+6A(n-1)(n大于等于2,n属于整整数)若数列{A(n+1)+kAn}是等比数列.(1)求数列{An}的通项公式
(2)求证:1/A1+1/A2+...1/An
数列{An}满足A1=5,A2=5,A(n+1)=An+6A(n-1)(n≥2,n∈N*).若数列{A(n+1)+kAn}是等比数列已知数列{An}满足A1=5,A2=5,A(n+1)=An+6A(n-1)(n大于等于2,n属于整整数)若数列{A(n+1)+kAn}是等比数列.(1)求数列{An}的通项公式 (2)
(1)对于此题:x2=x+6 解x1=-2,x2=3,于是a[n+1]+2*a[n]=3(a[n]+2*a[n-1])
数列{a[n+1]+2a[n]}为等比数列
所以a[n+1]+2a[n]=5*3^n → a[n+1]-3^(n+1)=-2(a[n]-3^n)
很容易求出a[n]=3^n+2*(-2)^(n-1)
(2)
当k为奇数是
1/an=1/(3^n+2^n)
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