Find a closed form expression for the nth right riemann sum of this integral?

Partitioning the interval into equally-spaced subintervals gives rectangles of width and of heights determined by the right endpoints of each subinterval.

If , then , , and so on, up to . Because we're using the right endpoints, the approximation will consider

The definite integral is then approximated by



You have






To check that this is correct, let's make sure the sum converges to the exact value of the definite integral. As , you have the sum converging to .

Meanwhile,



so we're done.

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