Question

Exam 3, Problem 3

Series to Integral

The equations I'm talking about are in my comment below, as I don't think I can write equations in this question box.

1) How did he come up with the interval [0,3] from looking at the series?

2) Why does he use f(x)=(1+x)^2? It certainly bears some resemblance to the series, but how did he arrive here... and how does 3/n = dx?

Thanks!

Answer 1

Here's the equation: \[\lim_{n \rightarrow \infty}\sum_{i=1}^{n}(1+i*3/n)^23/n\]=\[\int\limits_{0}^{3}(1+x)^2dx\]
The notion of a Riemann sum i familiar to me, and the integration is not at all difficult, I just want to know how he moved from the series to the integral.