Not able to understand case of inifinite recursive calls

#1

How does just checking for 99 & 999 proves that sum of squares will always either go to 1 or start repeating ?

#2

@phadnis.anurag for example if we are considering 999 that means we are considering Largest 3 digit no. possible and if largest 3 digit is not going to infinity that means no. smaller than 999 will also not goto infinity.

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