I am having a confusion with left and right Riemann sums for the integral $\int_2^\infty 1/x^2 dx$.
We can compare this with the sum $\sum_{n=2}^\infty 1/ n^2 $. If we take the left Riemann sum then since the graph is decreasing we would have $1/2^2 + 1/3^2 + \cdots$ and the area would be bigger than the integral. However, if we take the right Riemann sum the sum would be smaller than the integral. But both seem to be represented by the same sum $\sum_{n=2}^\infty 1/ n^2 $. How can I reconcile this?