Another nice inequality...

25 Oct 07 23:43

25 Oct 07 23:43

n is an integer >1. Prove:

sqrt(1+sqrt(n+sqrt((n^2)+sqrt((n^3)+...+sqrt(n^n)))...) < n

Example: if n=3 we get

sqrt(1+sqrt(3+sqrt(9+sqrt(27)))) < 3

30 Oct 07 02:48

Originally posted by David113
sqrt(1+sqrt(3+sqrt(9+sqrt(27)))) < 3

Could it be written this way?

[(1+(3+(9+(27^1/2)^1/2)^1/2)^1/2)]^1/2 < 3

30 Oct 07 11:37

Originally posted by Drew L
Could it be written this way?

[(1+(3+(9+(27^1/2)^1/2)^1/2)^1/2)]^1/2 < 3

Yes