Question
It can be shown that for any positive integer n, the infinitely nested radical expression
(n+(n+(n+....)^1/2)^1/2)^1/2
equals a finite number. What is the largest positive integer n≤999 such that this expression is equal to a positive integer?
Details and assumptions
A nested radical expression is one which contains a radical inside another one, as in
((5^1/2)+3)^1/2
An infinitely nested radical expression is one in which the radicals continue to an infinite extent.
(n+(n+(n+....)^1/2)^1/2)^1/2
equals a finite number. What is the largest positive integer n≤999 such that this expression is equal to a positive integer?
Details and assumptions
A nested radical expression is one which contains a radical inside another one, as in
((5^1/2)+3)^1/2
An infinitely nested radical expression is one in which the radicals continue to an infinite extent.
Answers
I AM AWESOME !!!
SO WHAT'S the Correct Answer ??
Dr cao
991
I AM AWESOME !!!
991 us wrong !!!
Dr cao
992