Question

I need help understanding how the integral test for infinite series works. It makes sense to me, but how do I set it up so that I have the excess on the left or right side of the curve? For instance, I know that for the sum of 1/k I need to get the sum so that it looks like it's larger than the integral from 1 to infinity of 1/x, but I don't know how to do that.

Answer 1

\[ \int_{1}^{\infty} 1/x dx \] gives the area of the curve bound by 1/x from 1 to infinity, if it is finite then summation of 1/x from 1 to infinity must be must converge .... same goes to the opposite logic.