Category:Cauchy Integral Test

This category contains pages concerning Cauchy Integral Test:

Let $f$ be a real function which is continuous, positive and decreasing on the interval $\hointr 1 {+\infty}$.

Let the sequence $\sequence {\Delta_n}$ be defined as:

$\ds \Delta_n = \sum_{k \mathop = 1}^n \map f k - \int_1^n \map f x \rd x$

Then $\sequence {\Delta_n} $ is decreasing and bounded below by zero.

Hence it converges.