Question

Determine whether the sequence is increasing, decreasing

Answer 1

\[a_{n} = n e ^{-n}\]

Answer 2

i can see tis is decreasing...but dunno how to prove it ....any idea ?

Answer 3

Try To rewrite it..

Answer 4

e^-n.... means 1\e^n

Answer 5

\[\frac{a_{n+1}}{a_n}=\frac{(n+1)e^{-(n+1)}}{ne^{-n}}=\frac{n+1}{e}\]
\[a_2<a_1\]

Answer 6

a2?

Answer 7

where did you get a2 from lol? :)

Answer 8

thanks...he mean a
n+1

Answer 9

oh, lol, atleast you got it ^_^

Answer 10

thanks all.. ^ ^ how bout this question.. \[a _{n} = n ^{n} / n!\]

Answer 11

ratio test ^_^

Answer 12

i using the method as up there...but getting complicated as i implant it

Answer 13

are you sure? it seems simple

an+1 /an :) give it a one more try

Answer 14

i get this.. \[a _{n+1} \div a _{n} = n+1 / n ^{n}\]

Answer 15

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

Answer 16

i getting that after simplified.. thsoe

Answer 17

alright, let's do it the easier way, take points for n and see whether it's increasing or decreasing :)

Answer 18

if the number is getting bigger then it's diverging, if the number is getting smaller then it's converging :)

Answer 19

ok..my bad..i found the answer..thanks

Answer 20

np ^_^