已知数列an满足a1=1/4,an=a[n-1]/(-1)^n•a[n-1]-2已知数列{a[n]}满足a1=1/4,an=a[n-1]/(-1)^n•a[n-1]-2(n大于等于2,n属于N)⑴求数列{a[n]}的通项公式a[n]⑵设[bn]=1/a[n]^2,求数列{b[n]}的前n项
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![已知数列an满足a1=1/4,an=a[n-1]/(-1)^n•a[n-1]-2已知数列{a[n]}满足a1=1/4,an=a[n-1]/(-1)^n•a[n-1]-2(n大于等于2,n属于N)⑴求数列{a[n]}的通项公式a[n]⑵设[bn]=1/a[n]^2,求数列{b[n]}的前n项](/uploads/image/z/7873843-67-3.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97an%E6%BB%A1%E8%B6%B3a1%3D1%EF%BC%8F4%2Can%3Da%5Bn-1%5D%EF%BC%8F%EF%BC%88-1%EF%BC%89%5En%26%238226%3Ba%5Bn-1%5D-2%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ba%5Bn%5D%7D%E6%BB%A1%E8%B6%B3a1%3D1%EF%BC%8F4%2Can%3Da%5Bn-1%5D%EF%BC%8F%EF%BC%88-1%EF%BC%89%5En%26%238226%3Ba%5Bn-1%5D-2%EF%BC%88n%E5%A4%A7%E4%BA%8E%E7%AD%89%E4%BA%8E2%2Cn%E5%B1%9E%E4%BA%8EN%EF%BC%89%E2%91%B4%E6%B1%82%E6%95%B0%E5%88%97%7Ba%5Bn%5D%7D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8Fa%5Bn%5D%E2%91%B5%E8%AE%BE%5Bbn%5D%3D1%EF%BC%8Fa%5Bn%5D%5E2%2C%E6%B1%82%E6%95%B0%E5%88%97%7Bb%5Bn%5D%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9)
已知数列an满足a1=1/4,an=a[n-1]/(-1)^n•a[n-1]-2已知数列{a[n]}满足a1=1/4,an=a[n-1]/(-1)^n•a[n-1]-2(n大于等于2,n属于N)⑴求数列{a[n]}的通项公式a[n]⑵设[bn]=1/a[n]^2,求数列{b[n]}的前n项
已知数列an满足a1=1/4,an=a[n-1]/(-1)^n•a[n-1]-2
已知数列{a[n]}满足a1=1/4,an=a[n-1]/(-1)^n•a[n-1]-2(n大于等于2,n属于N)
⑴求数列{a[n]}的通项公式a[n]
⑵设[bn]=1/a[n]^2,求数列{b[n]}的前n项和s[n]
过程详细符号什么的要清楚些~谢谢❤
已知数列an满足a1=1/4,an=a[n-1]/(-1)^n•a[n-1]-2已知数列{a[n]}满足a1=1/4,an=a[n-1]/(-1)^n•a[n-1]-2(n大于等于2,n属于N)⑴求数列{a[n]}的通项公式a[n]⑵设[bn]=1/a[n]^2,求数列{b[n]}的前n项
1.an=a[n-1]/(-1)^n•a[n-1]-2(n大于等于2,n属于N)
1/a(n)=(-1)^n-2/a(n-1)
1/a(n+1)=(-1)^(n+1)-2/a(n)
1/a(n+1)+1/a(n)=-2(1/a(n-1)+1/a(n))
[1/a(n+1)+1/a(n)]/[1/a(n-1)+1/a(n)]=-2
所以数列{1/a(n+1)+1/a(n)}为等比数列,公比q=-2
1/a(n+1)+1/a(n)=[1/a(2)+1/a(1)]q^(n-1)
a(1)=1/4,a(2)=-1/7
1/a(n+1)+1/a(n)=3*(-2)^(n-1)/28
(-1)^(n+1)-2/a(n)+1/a(n)=3*(-2)^(n-1)/28
a(n)=28/[(-1)^(n-1)(28-3*2^(n-1)]
2.b(n)=1/(a(n)^2)=28^2/(28-3*2^(n-1))^2
1/b(n)=(1-3*2^(n-1)/28)^2
1/b(n+1)=(1-3*2^n/28)^2
b(n+1)/b(n)=[(1-3*2^(n-1))(1-3*2^n)]^2
b(n+2)/b(n+1)=[(1-3*2^n)(1-3*2^(n+1)]^2
所以数列{b(n)}为等比数列
b(1)=16,b(2)=49
b(n)=16*(49/16)^(n-1)
s(n)=16(1-(16/49)^(n-1)/(1-16/49)=784(1-(16/49)^n)/33