My Math Forum Series Convergence

 Calculus Calculus Math Forum

 October 30th, 2016, 07:09 AM #1 Member   Joined: Aug 2016 From: illinois Posts: 46 Thanks: 0 Series Convergence If you are using the integral test to find if a series is convergent or divergent, and find the integral converges to a negative number, does that mean the series still converges.
 October 30th, 2016, 07:24 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,385 Thanks: 2476 Math Focus: Mainly analysis and algebra The integral test operates on positive, monotonic functions only (from memory). You should investigate the integral of $|f(x)|$ to see if the series is absolutely convergent. Last edited by v8archie; October 30th, 2016 at 07:30 AM.
 October 31st, 2016, 07:21 AM #3 Senior Member   Joined: Mar 2015 From: New Jersey Posts: 1,444 Thanks: 106 Integral Test Let f(x) be positive, continuous , and non-increasing for x$\displaystyle \geq$ N and a$\displaystyle _{n}$ =f(n) for n$\displaystyle \geq$N. Then a$\displaystyle _{n}$ converges or diverges according as $\displaystyle \int_{N}^{\infty}$f(x)dx converges or diverges.

 Tags convergence, series

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Johanovegas Calculus 2 January 23rd, 2016 01:34 PM Luiz Real Analysis 1 May 10th, 2015 09:38 AM Kreiger Real Analysis 5 April 19th, 2015 03:09 PM walter r Real Analysis 3 April 5th, 2014 08:50 PM aaron-math Calculus 4 February 20th, 2013 03:29 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top