0.999... can be reduced to the following infinitely long series:
0.9 + 0.09 + 0.009 + 0.0009 ...
This can be further reduced to:
0.9 + (0.9 * 0.1) + (0.9 * 0.1 * 0.1) + (0.9 * 0.1 * 0.1 * 0.1) ...
This series follows the general pattern of infinite series, and so we can use the infinite sum formula to work out the total:
Total = a / (1 - r)
a being 0.9
r being 0.1
So, the sum of the infinite series obtained from breaking down 0.999... is:
0.999... = 0.9 / 1 - 0.1
0.999... = 0.9 / 0.9
0.999... = 1
Q. E. fuckin' D. bitches. (again)
0.9 + 0.09 + 0.009 + 0.0009 ...
This can be further reduced to:
0.9 + (0.9 * 0.1) + (0.9 * 0.1 * 0.1) + (0.9 * 0.1 * 0.1 * 0.1) ...
This series follows the general pattern of infinite series, and so we can use the infinite sum formula to work out the total:
Total = a / (1 - r)
a being 0.9
r being 0.1
So, the sum of the infinite series obtained from breaking down 0.999... is:
0.999... = 0.9 / 1 - 0.1
0.999... = 0.9 / 0.9
0.999... = 1
Q. E. fuckin' D. bitches. (again)
