English is my second language:

I want to increase the accuracy of the trapezoidal rule for approximating the area beneath a curve by increasing the number of trapeziums the area is segregated into.

My problem is I have very limited knowledge of how to use the sigma function. This is what I have so far:

Area of trapezium = lim(Δx->0) 1/2*Δx*(f(x)+f(x+Δx)) where f(x) is some function of x.

My justification is that by making the Δx very small, the area must be segregated into more trapeziums but Iknowthat this is only half of the solution that I desire - how do I fit this into a sigma function and what constraints do I use?