Thread: Integral Test

Use the integral test to determine if the given series is convergent or divergent.

the sum from k=1 to infinity of e^k / (2+e^k)


math, math, math...

the limit as b approaches infinity of [lnb-ln1]

-ln1 = 0

the limit approaches 0, so the series is convergent.


Does this look correct?

Hello,

Wooo, how did you get that ? Plus, unfortunately,

What is ?

I am pretty sure this one is divergent.

Ok, let's see...

limit as b approaches infinity (from 1 to b) of e^x/(2+e^x)

u = 2 + e^x
du = e^x

so, by substitution method,

limit as b approaches infinity (from 1 to b) of 1/u du

limit as b approaches infinity (from 1 to b) of[lnu + c]

limit as b approaches infinity of [lnb - ln1]

so, since ln(infinity) = infinity and ln1 = 0, does that mean that the series diverges?

...or am I totally off?

Originally Posted by Foxtenn5

Ok, let's see...

limit as b approaches infinity (from 1 to b) of e^x/(2+e^x)

u = 2 + e^x
du = e^x

so, by substitution method,

limit as b approaches infinity (from 1 to b) of 1/u du

limit as b approaches infinity (from 1 to b) of[lnu + c]

limit as b approaches infinity of [lnb - ln1]

so, since ln(infinity) = infinity and ln1 = 0, does that mean that the series diverges?

...or am I totally off?

This is it