Hello,
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?
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?