Both approach π, but their rates of convergence are very different
There are many series that approach π as more terms are added. But the number of terms needed to reach a given level of accuracy varies greatly from one series to another. Race the Leibniz and Nilakantha series side by side.
💡 The error of the Leibniz series decreases inversely proportional to the number of terms, so it converges very slowly (hundreds of terms are needed for three decimal places of accuracy). The Nilakantha series has an error that decreases inversely proportional to the cube of the number of terms, so it becomes accurate much faster — that is what different "rates of convergence" mean.