Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

Using the integral test, how do you show whether #1/(2n+3)# diverges or converges?

1 Answer

May 14, 2015

#int_1^oo 1/(2x+3) dx = lim_(brarroo) int_1^b 1/(2x+3) dx#

#= lim_(brarroo) 1/2 int_1^b 1/(2x+3) 2dx#

#= lim_(brarroo) 1/2 ln(2x+3)|_1^b #

#= lim_(brarroo) [1/2 ln(2b+3) - 1/2 ln5]#

The integral, and hence the series, diverges.

Related questions

What is the Integral Test for Convergence of an Infinite Series?
How do you know when to use the integral test for an infinite series?
How do you use the Integral test on the infinite series #sum_(n=1)^oo1/root5(n)# ?
How do you use the Integral test on the infinite series #sum_(n=1)^oo1/n^5# ?
How do you use the Integral test on the infinite series #sum_(n=1)^oo1/(2n+1)^3# ?
How do you use the Integral test on the infinite series #sum_(n=1)^oo1/sqrt(n+4)# ?
How do you determine if the series #ln(1/2) + ln(1/3) + ln(3/4) + ... +ln[k/(k + 1)] + ....# converges?
How do you know #{-1,1,-1,1,-1,1,...}# converges or diverges?
Using the integral test, how do you show whether # (1 + (1/x))^x# diverges or converges?
Using the integral test, how do you show whether #sum 1/(n^2+1)# diverges or converges from n=1...

See all questions in Integral Test for Convergence of an Infinite Series

Impact of this question

5266 views around the world

You can reuse this answer
Creative Commons License