# Thread: Integral Test

1. ## 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?

2. Hello,

$\lim_{b \to +\infty} \ln(b)=+\infty \neq 0$

3. Wooo, how did you get that $[\ln b-\ln 1]$ ? Plus, unfortunately, $\lim_{b\to\infty}\ln b= \infty$

What is $\int_1^b\frac{\exp x}{2+\exp x}\,\mathrm{d}x$ ?

4. $\int_{1}^{\infty}\frac{e^{k}}{2+e^{k}}dk={\infty}$

I am pretty sure this one is divergent.

5. 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?

6. 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