<p>alright, tell me if this diverges:</p>
<p>sum(e^x / (e^x + 1) ) where x is from 1 to infinity</p>
<p>i thought it diverges when the limit of the function does not equal zero. well, this limit equals one, but when i put it into my ti-89, it did not give me infinity like it usually does when series diverge...so please explain. thanks!</p>
<p>Well at infinity the +1 means nothing, so you have a limit of 1 = ((e^x)/(e^x)), which means this = a whole number so it doesn't diverge. </p>
<p>How do you do the TI-89 thing?</p>
<p>i just did the sum thing under the calculus menu. f3 on the home screen. and i got the limit part, that's why i was wondering if it was divergent.</p>
<p>wait so what is the rule for the divergence of a series when you take the limit? i thought it diverges if the limit does not equal zero?</p>
<p>you guys don't know your calculus very well
Nth term divergence test: the series diverges if the limit as x -> infinity does NOT equal 0
in this case, the limit of the sequence does NOT equal 0, so it's a divergent series. it's really common sense. think about it, if the limit as x-> infinity of the sequence is anything besides 0, then when you take the summation of that, you'll be adding up an infinite amount of constants, which is obviously divergent. don't listen to your calculator, use your brain.</p>
<p>The lim = 1, so it diverges.</p>
<p>woah ho ho, mr. calculus. thank you i got the limit part. i'm not stupid. i was just wondering why my calculator didn't give me infinity. good lord. but of course i'm just a meager little ab student trying to study for bc. i MUST not know my calculus very well.</p>
<p>thank you 4orce, that was directed towards sk33tast1c, to whom i pale in comparison obviously.</p>
<p>Calculators only have an IQ of 9999999999. Its not the calculator's fault!!!</p>