已知数列{an}中,a1=-1,a2=2,且an+1+an-1=2(an +1)(n≥2,n∈N已知数列{an}中,a1=-1,a2=2,且an+1+an-1=2(an +1)(n≥2,n∈N+).求证:1)数列{an-an-1}为等差数列 (2)求通项an注,a的旁边是角标,比a小,如n+1等,电脑不知道
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![已知数列{an}中,a1=-1,a2=2,且an+1+an-1=2(an +1)(n≥2,n∈N已知数列{an}中,a1=-1,a2=2,且an+1+an-1=2(an +1)(n≥2,n∈N+).求证:1)数列{an-an-1}为等差数列 (2)求通项an注,a的旁边是角标,比a小,如n+1等,电脑不知道](/uploads/image/z/5527650-66-0.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ban%7D%E4%B8%AD%2Ca1%3D-1%2Ca2%3D2%2C%E4%B8%94an%2B1%2Ban-1%3D2%28an+%2B1%29%28n%E2%89%A52%2Cn%E2%88%88N%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ban%7D%E4%B8%AD%2Ca1%3D-1%2Ca2%3D2%2C%E4%B8%94an%2B1%2Ban-1%3D2%28an+%2B1%29%28n%E2%89%A52%2Cn%E2%88%88N%2B%29.%E6%B1%82%E8%AF%81%EF%BC%9A1%29%E6%95%B0%E5%88%97%7Ban-an-1%7D%E4%B8%BA%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97+%EF%BC%882%EF%BC%89%E6%B1%82%E9%80%9A%E9%A1%B9an%E6%B3%A8%2Ca%E7%9A%84%E6%97%81%E8%BE%B9%E6%98%AF%E8%A7%92%E6%A0%87%2C%E6%AF%94a%E5%B0%8F%2C%E5%A6%82n%2B1%E7%AD%89%2C%E7%94%B5%E8%84%91%E4%B8%8D%E7%9F%A5%E9%81%93)
已知数列{an}中,a1=-1,a2=2,且an+1+an-1=2(an +1)(n≥2,n∈N已知数列{an}中,a1=-1,a2=2,且an+1+an-1=2(an +1)(n≥2,n∈N+).求证:1)数列{an-an-1}为等差数列 (2)求通项an注,a的旁边是角标,比a小,如n+1等,电脑不知道
已知数列{an}中,a1=-1,a2=2,且an+1+an-1=2(an +1)(n≥2,n∈N
已知数列{an}中,
a1=-1,a2=2,且an+1+an-1=2(an +1)(n≥2,n∈N+).
求证:1)数列{an-an-1}为等差数列 (2)求通项an
注,a的旁边是角标,比a小,如n+1等,电脑不知道怎么小写
已知数列{an}中,a1=-1,a2=2,且an+1+an-1=2(an +1)(n≥2,n∈N已知数列{an}中,a1=-1,a2=2,且an+1+an-1=2(an +1)(n≥2,n∈N+).求证:1)数列{an-an-1}为等差数列 (2)求通项an注,a的旁边是角标,比a小,如n+1等,电脑不知道
a(n+1) + a(n-1) = 2a(n) + 2,
a(n+1) - a(n) = a(n) - a(n-1) + 2,
a(n+2) - a(n+1) = a(n+1) - a(n) + 2,
{a(n+1)-a(n)}是首项为a(2)-a(1)=3,公差为2的等差数列.
a(n+1)-a(n) = 3 + 2(n-1) = 2n + 1 = n(n+1)-(n-1)n + (n+1)-n,
a(n+1) - n(n+1) - (n+1) = a(n) - (n-1)n - n,
{a(n) - (n-1)n - n}是首项为a(1) - 0 - 1 = -2,的常数数列.
a(n) - (n-1)n - n = -2,
a(n) = (n-1)n+n-2 = n^2 - 2