by Guest Sat Oct 29, 2011 2:39 pm
NZG wrote: Rei Andros wrote:I drunkenly stumbled back onto the forum.
Can't say I'll be able to solve it but I'll give it a crack.
Just saw the HP deleted screen with Lupin and Tonks.
Find the limit of the sequence as n goes to infinity
n=(ln(n+1)^2)/(n^2)
There are no typos and best thing is.
No answer for it..
lim n->inf (ln(n+1)^2)/(n^2)
It's been a long time but I think you should apply L'Hospital's Rule. If you plug in the limit you get what's called infinity/infinity form. L'Hospital's Rule allows you to take the derivative of the function in this case.
By taking the derivative you get:
lim n->inf (ln(n+1)^2)/(n^2) = [2(n+1)]/(n+1)^2/2n
Simplify
lim n->inf (ln(n+1)^2)/(n^2) = 1/(n^2+1)
Divide the top and bottom by n^2
lim n->inf (ln(n+1)^2)/(n^2) = 1/n^2/(1+1/n^2)
Now plug in the limit again. Both 1/n^2 terms go to zero so the answer should be zero.