# Error estimation integral test

##### *2020-02-21 06:52*

Stack Exchange network consists of 175 Q& A communities including Stack Overflow, the largest, most trusted online community for developers to learn, shareThus the series and the integral converge or diverge together. For a convergent series (or any convergent series satisfying the criteria of the integral test), the inequality holds for all, error estimation integral test

Also, it is clear that f(x) 0 for all x 2. To see that it is decreasing, we compute its derivative: f0(x) (lnx)2 2lnx x2(lnx)4. ; and since f0(x) 0 for all x 2, the function in decreasing. Thus all the conditions of the integral test are satis ed.