Infinite decimal

Imagine the infinite decimal number 0.99999999 .. ... ... ... That is a decimal and her endless serie of nines. Determine how much this number is less than the number 1. Thank you in advance.

Correct result:

x =  0

Solution:

a1=0.9 q=0.1 s=a1/(1q)=0.9/(10.1)=1 x=1s=11=0a_{1}=0.9 \ \\ q=0.1 \ \\ s=a_{1} / (1-q)=0.9 / (1-0.1)=1 \ \\ x=1-s=1-1=0



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