Sum[(1/(4 (n^2)-1)),{n,1,∞}]

Sum[((2^(-n))/(n(n+1))),{n,1,∞}]

Sum[((((-2))^(-n))/(n(n+1))),{n,1,∞}]

Sum[((((-3))^(-n))/(2n+1)),{n,0,∞}]

Sum[(1/(n(2 n+1))),{n,1,∞}]

Sum[((2^(-n))/(2 n+1)),{n,1,∞}]

FullSimplify[Sum[((n+2)/(n (n+1)(2^n))),{n,1,∞}]]

Sum[((2 (n^2)-5n-1)/(2^n)),{n,0,∞}]

Sum[((15 (n^2)-4n+1)/(2^n)),{n,0,∞}]

Sum[(1/(n(2 n+1))),{n,1,∞}]

Sum[(1/((2n+1)(3 n+2))),{n,0,∞}]

Sum[((((-1))^n)/((3n+1)(3 n+2))),{n,0,∞}]

Sum[(((((-1))^n)(2n+1))/((3n+1)(3 n+2))),{n,0,∞}]

Sum[((((-1))^n)/((2n+1)(3 n+2))),{n,0,∞}]

Together[D[(((t-3)(t+3))/(10-2 (Sqrt[3]) t)),t]]

Solve[1==(((t^2)-9)/(10-2 (Sqrt[3]) t)),t]