### Brain Teasers

# To Infinity and Beyond!

In the function f(x), f(x) equals the sum of the digits of x and the sum of the new number's digits and so on until one digit is remaining. For example:

f(787)=f(7+8+7)=f(22)=f(2+2)=f(4)=4

and

f(9135899)=f(9+1+3+5+8+9+9)= f(44)=f(4+4)=f(8)=8

So, if we assume that infinity is equal to 9999999999999... with an infinite amount of digits, then what is f(infinity)?

f(787)=f(7+8+7)=f(22)=f(2+2)=f(4)=4

and

f(9135899)=f(9+1+3+5+8+9+9)= f(44)=f(4+4)=f(8)=8

So, if we assume that infinity is equal to 9999999999999... with an infinite amount of digits, then what is f(infinity)?

### Answer

f(infinity)=9Any number with all nines for digits will all add up to nine:

f(9)=9

f(99)=f(18)=f(9)=9

f(999)=f(27)=f(9)=9

f(99999999999999)=f(126)=f(9)=9

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