#### Posers and Puzzles

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

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- 01 May '07
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- 27311

*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

*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