AM GM inequality help

  • Thread starter The legend
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  • #1
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Homework Statement



Prove

a)5 < 51/2 + 51/3 + 51/4

b) n > n1/2 + n1/3 + n1/4 for all ints n>8

Homework Equations





The Attempt at a Solution


i tried the AM GM inequality
and found

51/2 + 51/3 + 51/4 > 3(513/36)

what further can i do?
can anyone please help me out??
 

Answers and Replies

  • #2
35,017
6,766


Homework Statement



Prove

a)5 < 51/2 + 51/3 + 51/4

b) n > n1/2 + n1/3 + n1/4 for all ints n>8

Homework Equations





The Attempt at a Solution


i tried the AM GM inequality
and found

51/2 + 51/3 + 51/4 > 3(513/36)
> 3 * 51/3 = (27 * 5)1/3

Can you show that the last expression is > 5?
what further can i do?
can anyone please help me out??
 
  • #3
424
0


Thanks
so i got that part and showed the expression > 5.

I could prove the 2nd part by this method too!

Thanks a lot!!! :smile:
 

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