integraalitestiä
Integraalitestiä, also known as the integral test, is a mathematical tool used in calculus to determine the convergence or divergence of an infinite series. The test applies to series of positive terms. Specifically, if f(x) is a continuous, positive, and decreasing function on the interval [n, infinity) and a_n = f(n) for all integers n, then the infinite series sum from n=1 to infinity of a_n converges if and only if the improper integral from 1 to infinity of f(x) dx converges.
The core idea behind the integral test is to compare the sum of the series to the
It is crucial that the function f(x) meets all the conditions of the integral test: continuity, positivity,