已知数列{an}满足an+1=(3an+1)/(an+3),a1=-1/3 求证1/(an)+1为等差数列,求an题目错了……重发已知数列{an}满足an+1=(an-1)/(an+3),a1=-1/3 求证1/(an)+1为等差数列,求an
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![已知数列{an}满足an+1=(3an+1)/(an+3),a1=-1/3 求证1/(an)+1为等差数列,求an题目错了……重发已知数列{an}满足an+1=(an-1)/(an+3),a1=-1/3 求证1/(an)+1为等差数列,求an](/uploads/image/z/2680727-23-7.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ban%7D%E6%BB%A1%E8%B6%B3an%2B1%3D%283an%2B1%29%2F%28an%2B3%29%2Ca1%3D-1%2F3+%E6%B1%82%E8%AF%811%2F%28an%29%2B1%E4%B8%BA%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E6%B1%82an%E9%A2%98%E7%9B%AE%E9%94%99%E4%BA%86%E2%80%A6%E2%80%A6%E9%87%8D%E5%8F%91%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ban%7D%E6%BB%A1%E8%B6%B3an%2B1%3D%28an-1%29%2F%28an%2B3%29%EF%BC%8Ca1%3D-1%2F3+%E6%B1%82%E8%AF%811%2F%28an%29%2B1%E4%B8%BA%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%EF%BC%8C%E6%B1%82an)
已知数列{an}满足an+1=(3an+1)/(an+3),a1=-1/3 求证1/(an)+1为等差数列,求an题目错了……重发已知数列{an}满足an+1=(an-1)/(an+3),a1=-1/3 求证1/(an)+1为等差数列,求an
已知数列{an}满足an+1=(3an+1)/(an+3),a1=-1/3 求证1/(an)+1为等差数列,求an
题目错了……重发
已知数列{an}满足an+1=(an-1)/(an+3),a1=-1/3 求证1/(an)+1为等差数列,求an
已知数列{an}满足an+1=(3an+1)/(an+3),a1=-1/3 求证1/(an)+1为等差数列,求an题目错了……重发已知数列{an}满足an+1=(an-1)/(an+3),a1=-1/3 求证1/(an)+1为等差数列,求an
a(n+1)=[a(n)-1]/[a(n)+3],
a(n+1)+1=[a(n)-1]/[a(n)+3] +1=[2a(n)+2]/[a(n)+3]=2[a(n)+1]/[a(n)+3],
若a(n+1)+1=0,则a(n)+1=0,...,a(1)+1=0,与a(1)=-1/3矛盾.
因此,a(n)+1 不为0.
1/[a(n+1)+1] = [a(n)+3]/[2a(n)+2] = [a(n)+1+2]/[2a(n)+2] = 2/[2a(n)+2] + [a(n)+1]/[2a(n)+2]
=1/[a(n)+1] + 1/2,
{1/[a(n)+1]}是首项为1/[a(1)+1]=1/[1-1/3]=3/2,公差为1/2的等差数列.
1/[a(n)+1] = 3/2 +(n-1)/2 = (n+2)/2,
a(n)+1=2/(n+2),
a(n)=2/(n+2) - 1 = -n/(n+2)