anonymous
  • anonymous
Determine whether the sequence is increasing, decreasing
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[a_{n} = n e ^{-n}\]
anonymous
  • anonymous
i can see tis is decreasing...but dunno how to prove it ....any idea ?
anonymous
  • anonymous
Try To rewrite it..

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anonymous
  • anonymous
e^-n.... means 1\e^n
nikvist
  • nikvist
\[\frac{a_{n+1}}{a_n}=\frac{(n+1)e^{-(n+1)}}{ne^{-n}}=\frac{n+1}{e}\] \[a_2
anonymous
  • anonymous
a2?
anonymous
  • anonymous
where did you get a2 from lol? :)
anonymous
  • anonymous
thanks...he mean a n+1
anonymous
  • anonymous
oh, lol, atleast you got it ^_^
anonymous
  • anonymous
thanks all.. ^ ^ how bout this question.. \[a _{n} = n ^{n} / n!\]
anonymous
  • anonymous
ratio test ^_^
anonymous
  • anonymous
i using the method as up there...but getting complicated as i implant it
anonymous
  • anonymous
are you sure? it seems simple an+1 /an :) give it a one more try
anonymous
  • anonymous
i get this.. \[a _{n+1} \div a _{n} = n+1 / n ^{n}\]
anonymous
  • anonymous
no dear , you'll get something like this: an+ 1 = (n+1)^(n+1)/(n+1) ! then divide this with an, give it a try
anonymous
  • anonymous
i getting that after simplified.. thsoe
anonymous
  • anonymous
alright, let's do it the easier way, take points for n and see whether it's increasing or decreasing :)
anonymous
  • anonymous
if the number is getting bigger then it's diverging, if the number is getting smaller then it's converging :)
anonymous
  • anonymous
ok..my bad..i found the answer..thanks
anonymous
  • anonymous
np ^_^

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