Skip to main content
1 of 5
Eric Naslund
  • 11.4k
  • 1
  • 66
  • 106

The sums above are Riemann sums for the function $\arctan(x)$ between $x=0$ and $x=1$, so the limit will equal the integral which is $\frac{\pi}{4}$. The reason both of these converge to the same value is because in both cases is because the lengths of the intervals go to zero.

Eric Naslund
  • 11.4k
  • 1
  • 66
  • 106