calculus question?

Question

Determine if the sequence converges or diverges. If it converges, find the limit: ln(n)/ln(2n)

Answer 1

you have not specified n so I presume inf
in n /in(2n)
= ln n/(ln n + in 2)
= 1/(1+ ln 2/lm n)
as n ->inf denominator->1 so limit is 1

Answer 2

If n -> 00, the limit is 1.
You can use L'Hopital:
Ln n / Ln 2n = 1/n / 2/2n = 1

Answer 3

it converges - though rather slowly, as often with logarithms.

to calculate the limit you can use L'Hopital's rule which state that the limit for f(x)/g(x) will be equal, under certain circumstances (valid here) to the limit for f'(x)/g'(x). Which will give you 1 for n approaching infinity in your question.

a

Answer 4

At n=1/2 it is discontinuous & changes from infinity to minus infinity and then lim to infinity it converges to 1

Answer 5

it converges to 0.....because ln n

Answer 6

You can find the equation for the ln series (taylor series) and then evaluate or just graph both equations and look at the picture.

Answer 7

ln(2n)=ln(2)+ln(n)
Therefore lim ln(n)/ln(2n)=lim ln(n)/(ln(2)+ln(n))=1
assuming that the limit is as n goes to infinity.

Answer 8

it converges to one at infinity. just take the limit.