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

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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.

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