# Thread: Does anyone have general strategies for converting a Riemann sum to a integral?

1. ## Does anyone have general strategies for converting a Riemann sum to a integral?

I need to deal some of question of this type recent,but I always get stuck.
ex.
$\sum_{m=k}^{(tk^2)/2}\frac{1}{\sqrt{(\pi\frac{tk^2}{2})}}*exp{\frac{-m^2}{2tk^2}}$
tons of thanks in advance,if anyone has ideas

my teacher said it approximately equals to $\sqrt{\frac{2}{\pi}}\int_{\frac{1}{\sqrt{t}}}^{inf inity} e^{-x^{2}}\,dx$

but I have no idea how to convert it.

2. ## Re: Does anyone have general strategies for converting a Riemann sum to a integral?

Originally Posted by kimkim007
I need to deal some of question of this type recent,but I always get stuck.
ex.
$\sum_{k=0}^{(tk^2)/2}((1/sqrt{(pi*(tk^2)/2)}*exp{-(m^2)/(2tk^2)}$
tons of thanks in advance,if anyone has ideas
A "Riemann sum" is always of the form $\sum_{k=0}^N f(x_k)\Delta_k$ and the reduces to the integral $\int_{f(x_0)}^{f(x_N)} f(x)dx$.
Basically, what you need to do is determine which part of the sum you want to be " $f(x_k)$" and which part you want to be " $\delta_k$".

However, you " $tk^2/2$" as the upper limit as your sum. That is impossible. You cannot have "k", the sum index in the upper limit.

3. ## Re: Does anyone have general strategies for converting a Riemann sum to a integral?

Thank for you reply Hallsoivy,I am new to latex,there is a typo in my original formula.

4. ## Re: Does anyone have general strategies for converting a Riemann sum to a integral?

HallsofIvy,I amend my thread. could you plz look at it again. I don't know how to convert one to other one.