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#### OhMyMarkov

##### Member

- Mar 5, 2012

- 83

Hello everyone!

I'm trying to show that $\lim \sup \sqrt[n]{c_{n+1}}=\lim \sup \sqrt[n]{c_n}$

This is my attempt:

$\lim \sup \sqrt[n]{c_{n+1}} = \lim \sup \sqrt[m-1]{c_m}=\lim \sup c_m \; ^{\frac{1}{m}}c_m \; ^{\frac{1}{m(m-1)}}$

I'm stuck here, I think I must use some exponential property that says that something decays faster than something or the ratio of two things is zero in the limit...

Any help is appreciated!

I'm trying to show that $\lim \sup \sqrt[n]{c_{n+1}}=\lim \sup \sqrt[n]{c_n}$

This is my attempt:

$\lim \sup \sqrt[n]{c_{n+1}} = \lim \sup \sqrt[m-1]{c_m}=\lim \sup c_m \; ^{\frac{1}{m}}c_m \; ^{\frac{1}{m(m-1)}}$

I'm stuck here, I think I must use some exponential property that says that something decays faster than something or the ratio of two things is zero in the limit...

Any help is appreciated!

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