Recent content by Newbie234

The first statement is false. But I am correct in assuming that the second statement implies that the infinite sums of f(x) and g(x) are asymptotically equivalent (that is, lim_{n->\infty}\frac{\sum^{n}_{x=0}f(x)}{\sum^{n}_{x=0}g(x)}=1).

Summing over integers. Also, are these statements true for continuous functions that aren't piecewise?

Sorry, thought it was pretty obvious, but I guess not. I didn't think it was necessary to add dx to the integrals or add that summation was over x as it was implied, and I didn't want to typeset anymore than I had to because it is new to me.

Let's say we have the statement \sum^{\infty}_{0}f(x)=\frac{\sum^{\infty}_{0}g(x)}{\sum^{\infty}_{0}h(x)} does this imply that \int^{\infty}_{0}f(x)=\frac{\int^{\infty}_{0}g(x)}{\int^{\infty}_{0}h(x)}? Also if \sum^{\infty}_{0}f(x)=\sum^{\infty}_{0}g(x) does this imply that f(x)=g(x), or...