>>585
① a_k = k･(3k-2) = 3k^2 -2k,
　s = 納k=1,n] a_k = 納k=1,n] (3k^2) - 納k=1,n] (2k) = …
② b_k = 納j=0,k-1] (3-1)･3^j = 納j=0,k-1] {3^(j+1) -3^j} = 3^k -1.
　s = 納k=1,n] b_k = 納k=1,n] {3^k -1} = …

>>593
　(1/2){tanh(x)+1} = sinh(x)/{2cosh(x)} + 1/2.
　1/{2(tanh(x)+1)} = cosh(x)/{2(sinh(x)+cosh(x))} = cosh(x)/{2exp(x)} = (1/4){1+exp(-2x)} なので…