Infinite Nested Square Roots


[ Formula Database ]

Added by Simon Strong on March 12, 2001 at 06:13:23:

2 = sqrt( 2 + sqrt( 2 + sqrt( 2 + sqrt ( .... ) ) ) )
3 = sqrt( 6 + sqrt( 6 + sqrt( 6 + sqrt ( .... ) ) ) )
5 = sqrt( 20 + sqrt( 20 + sqrt( 20 + sqrt ( .... ) ) ) )

and, in general,

n = sqrt( m + sqrt( m + sqrt( m + sqrt ( .... ) ) ) )

where n is an integer > 1, and m=n(n-1)