ok, the lim of the nth root of (1+3n) Thanks in advance!
"Qu'est-ce que c'est ?" ^^
If you want to know, you can remember that when dealing with power series and looking for the radius of convergence, you can choose between the ratio or the power test. Both will give the same result
Now, if you want to prove it, that's another matter lol
But where is the power series here? Is it meant to be $\displaystyle \sum (1 + 3n) x^n$ .....?
Originally Posted by Mathstud28
If $\displaystyle a_n = 1 + 3n$ then the ratio is wrong for a start.
By the way, regarding "By the connection between the root and ratio test" ...... What happens when you apply the ratio test and the nth root test to $\displaystyle \sum_{n=1}^{\infty} 2^{(-1)^n - n}$ .....?
Are you really going to be that semantical? Well to answer your question, I never said every limit can be done this way, what you provided is a case where the root test and the ratio test differ. What I am talking about is much more specific, it is
By the connection
$\displaystyle \lim_{n\to\infty}f(n)^{\frac{1}{n}}=\lim_{n\to\inf ty}\frac{f(n+1)}{f(n)}$
And $\displaystyle f(n)$ cannot have a variable exponent. I will post back later with a more in-depth reasoning.