$$\lim_{n\to \infty}\frac{3^n}{2^n+3^n}$$

Question

fibonaccichick666 · Answer

Do you know squeeze thm?

anonymous · Answer

i know it is one, i need a nice method

aravindg · Answer

How about taking 3^n common from denominatr

aravindg · Answer

nah ...wont work

fibonaccichick666 · Answer

I'd just drop the 2^n off for sqeeze

anonymous · Answer

squueze is good since 3^n is always < 3^n + 2^n

fibonaccichick666 · Answer

or divide everything by 3^n then simplify

anonymous · Answer

@FibonacciChick666  that looks good thanks

christos · Answer

go by derivatives d/(dn)2^-n

fibonaccichick666 · Answer

np if it's a math theory course the dividing by 3^n is a better approach.  for calc, I'd just use squeeze. :)

anonymous · Answer

not sure about squeeze though since $\frac{3^n}{2^n+3^n} <\frac{3^n}{3^n}$ but what goes on the other sides?

anonymous · Answer

i would just drop off the $2^n$ since it is not important, but still not sure how to use squeeze to get this

fibonaccichick666 · Answer

for squeeze can it =0?

anonymous · Answer

no

fibonaccichick666 · Answer

but that doesn't help hmmm

anonymous · Answer

if i you want to show it is one, you have to squeeze it between two things that are one

christos · Answer

attachment

fibonaccichick666 · Answer

could multiplying by the conjugate help?

anonymous · Answer

i like dividing by $3^n$ top and bottom
looks good to me

fibonaccichick666 · Answer

haha yea it works, but now I want to know how to do it using squeeze lol

fibonaccichick666 · Answer

btw how do you get your $$3^n$$ in line with your text?

anonymous · Answer

you would have to find some other function $g$ with $g(n)<\frac{3^n}{2^n+3^n}$ and also $\lim_{n\to \infty}g(n)=1$

anonymous · Answer

i use \( instead of \[

anonymous · Answer

if you want to see any code, right click and choose "show math as" then "latex"

fibonaccichick666 · Answer

thanks for that! and I'm thinking maybe $e^{-x}$

fibonaccichick666 · Answer

but no that's zero too

anonymous · Answer

yeah you have to get something that goes to one 
not really sure what it would be

fibonaccichick666 · Answer

hmmm... That is a head scratcher

fibonaccichick666 · Answer

maybe $\frac{x+1}{x-1}?$

fibonaccichick666 · Answer

yea, I think that works or it's inverse.  I like the inverse better actually.

e.mccormick · Answer