(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove

a)5 < 5^{1/2}+ 5^{1/3}+ 5^{1/4}

b) n > n^{1/2}+ n^{1/3}+ n^{1/4}for all ints n>8

2. Relevant equations

3. The attempt at a solution

i tried the AM GM inequality

and found

5^{1/2}+ 5^{1/3}+ 5^{1/4}> 3(5^{13/36})

what further can i do?

can anyone please help me out??

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# AM GM inequality help

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