(1)根据题意,有An=(An-An-1)+(An-1 - An-2)+…+(A2 - A1)+A1
=3-2^(2n-3) + 3-2^(2n-5) +…+(3-2^3)+ 2
再用分组求和法:
=3n - 【2^(2n-3)+2^(2n-5)+…2^3+2】
=3n-2*(1-4^n)(1-4)
=2*(1-4^n)3 + 3n
即An=-2*(4^n-1)3 + 3n
(2)Bn=n*An==-2n*(4^n-1)3 + 3n^2
与(1)同理:用分组求和法
帮我加分啦,我是新手喔
(1)根据题意,有An=(An-An-1)+(An-1 - An-2)+…+(A2 - A1)+A1
=3-2^(2n-3) + 3-2^(2n-5) +…+(3-2^3)+ 2
再用分组求和法:
=3n - 【2^(2n-3)+2^(2n-5)+…2^3+2】
=3n-2*(1-4^n)(1-4)
=2*(1-4^n)3 + 3n
即An=-2*(4^n-1)3 + 3n
(2)Bn=n*An==-2n*(4^n-1)3 + 3n^2
与(1)同理:用分组求和法
帮我加分啦,我是新手喔