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Posers and Puzzles

Posers and Puzzles

  1. 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
  2. 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
  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