# calculus and analysis – Calculating the convergence value of summation

Could you please tell me what value the left side of the inequality converges to?

`(H and P are constant values greater than 2 and n can go to infinity)`

$$sum_{n=1}^{inf}{left(H^n*left(frac{1}{P}right)^{frac{n(n-1)}{2}}right)}leq alpha$$

I know that according to d’Alembert’s ratio test the left side of inequality will converge to some value. as shown below:

Update: Thanks to @user64494 for the 3d plot I have another question

`Plot3D(NSum(H^n*(1/P)^(n*(n - 1)/2), {n, 1, Infinity}), {H, 2, 50}, {P, 2, 100})`

How can I change the out range? it only draws 0 to 200,