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
- Joined
- 01 May '07
- Moves
- 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
Cookies help us deliver our Services. By using our Services or clicking I agree, you agree to our use of cookies. Learn More.I Agree