怎么求递归函数的的通项公式?g(t)=[9*2^(t-1)-2]*g(t-1)/[3*2^(t-1)-2]+(9*2^t)*g(t-2)/[3*2^(t-1)-2]-(9*2^2t)*g(t-3)/{[3*2^(t-1)-2]*[3*2^(t-2)-2]}+[9*2^(2t-1)]*[3*(2^t)-3]/[3*2^(t-1)-2]+36*(2^2t)-27*2^t其中g(0)=12,g(1)=150,g(2)=
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![怎么求递归函数的的通项公式?g(t)=[9*2^(t-1)-2]*g(t-1)/[3*2^(t-1)-2]+(9*2^t)*g(t-2)/[3*2^(t-1)-2]-(9*2^2t)*g(t-3)/{[3*2^(t-1)-2]*[3*2^(t-2)-2]}+[9*2^(2t-1)]*[3*(2^t)-3]/[3*2^(t-1)-2]+36*(2^2t)-27*2^t其中g(0)=12,g(1)=150,g(2)=](/uploads/image/z/6952201-25-1.jpg?t=%E6%80%8E%E4%B9%88%E6%B1%82%E9%80%92%E5%BD%92%E5%87%BD%E6%95%B0%E7%9A%84%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%3Fg%28t%29%3D%5B9%2A2%5E%28t-1%29-2%5D%2Ag%28t-1%29%2F%5B3%2A2%5E%28t-1%29-2%5D%2B%289%2A2%5Et%29%2Ag%28t-2%29%2F%5B3%2A2%5E%28t-1%29-2%5D-%289%2A2%5E2t%29%2Ag%28t-3%29%2F%7B%5B3%2A2%5E%28t-1%29-2%5D%2A%5B3%2A2%5E%28t-2%29-2%5D%7D%2B%5B9%2A2%5E%282t-1%29%5D%2A%5B3%2A%282%5Et%29-3%5D%2F%5B3%2A2%5E%28t-1%29-2%5D%2B36%2A%282%5E2t%29-27%2A2%5Et%E5%85%B6%E4%B8%ADg%EF%BC%880%EF%BC%89%3D12%2Cg%EF%BC%881%EF%BC%89%3D150%2Cg%EF%BC%882%EF%BC%89%3D)
怎么求递归函数的的通项公式?g(t)=[9*2^(t-1)-2]*g(t-1)/[3*2^(t-1)-2]+(9*2^t)*g(t-2)/[3*2^(t-1)-2]-(9*2^2t)*g(t-3)/{[3*2^(t-1)-2]*[3*2^(t-2)-2]}+[9*2^(2t-1)]*[3*(2^t)-3]/[3*2^(t-1)-2]+36*(2^2t)-27*2^t其中g(0)=12,g(1)=150,g(2)=
怎么求递归函数的的通项公式?
g(t)=[9*2^(t-1)-2]*g(t-1)/[3*2^(t-1)-2]+(9*2^t)*g(t-2)/[3*2^(t-1)-2]-(9*2^2t)*g(t-3)/{[3*2^(t-1)-2]*[3*2^(t-2)-2]}+[9*2^(2t-1)]*[3*(2^t)-3]/[3*2^(t-1)-2]+36*(2^2t)-27*2^t
其中g(0)=12,g(1)=150,g(2)=1012
要的到g(t)的表达式,请给出完整的答案,
怎么求递归函数的的通项公式?g(t)=[9*2^(t-1)-2]*g(t-1)/[3*2^(t-1)-2]+(9*2^t)*g(t-2)/[3*2^(t-1)-2]-(9*2^2t)*g(t-3)/{[3*2^(t-1)-2]*[3*2^(t-2)-2]}+[9*2^(2t-1)]*[3*(2^t)-3]/[3*2^(t-1)-2]+36*(2^2t)-27*2^t其中g(0)=12,g(1)=150,g(2)=
题目是不是写错了啊,这样算出的g(3)不是整数.
解体思路可以告诉你,
首先令m(t)=3*2^(t-1)-2,这个式子就化成
g(t)=(3m+4)/m*g(t-1)+6(m+2)/m*g(t-2)-8(m+2)^2/[m(m-2)]*g(t-3)+4(5m+1)(m+1)/m
两边同乘m(t)(m(t)-2),得到
m(m-2)g(t)=(3m+4)(m-2)*g(t-1)+6(m+2)(m-2)*g(t-2)-8(m+2)^2*g(t-3)+4(5m+1)(m+1)(m-2)
注意到m[t]=2m[t-1]+2=4m[t-2]+6=8m[t-3]+14
令g(t)=Am(t)^3+Bm(t)^2+Cm(t)+D
带入后,将所有m[t]划为m[t-3]后整理为以m[t-3]为变量的多项式,
令所有项的系数为0即可解得A,B,C,D
从常数项可知D=-1/8,但是m(t)应该都是整数,所以是不是题目有问题啊