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a(1)=1,a(n+1)-a(n)=(1/3)^n,3^na(n+1) = 3*3^(n-1)a(n) + 1,3^na(n+1) + 1/2 = 3[3^(n-1)a(n) + 1/2]{3^(n-1)a(n) + 1/2}是首项为a(1)+1/2=3/2, 公比为3的等比数列。3^(n-1)a(n) + 1/2 = (3/2)3^(n-1) = (1/2)3^n,3^(n-1)a(n) = [3^n - 1]/2,a(n) = [3 - 1/3^(n-1)]/2.b(n) = (2n-1)a(n) = (2n-1)[3 - 1/3^(n-1)]/2 = (3/2)(2n-1) - [(2n-1)/2](1/3)... |
