Let denotes the square of the sum of the digits of natural number

MATHEMATICS · Subjective · CBSE · Mathematics · Number Play · Number Play

Problem

Let

f(n)

denotes the square of the sum of the digits of natural number

n

, where

f^2(n)

denotes

f(f(n))

f^3(n)

denotes

f(f(f(n)))

and so on. The value of

\frac{f^{2011}(2011) - f^{2010}(2011)}{f^{2013}(2011) - f^{2012}(2011)} \text{ is .....}