06/11/05 10:25:14
0.1+0.9=(1ｰ0.9)+0.9
0.01+0.99=(1ｰ0.99)+0.99
0.001+0.999=(1ｰ0.999)+0.999
0.0001+0.9999=(1ｰ0.9999)+0.9999
0.000…1+0.999…9=(1ｰ0.999…9)+0.999…9
lim[m→∞]
{Π[n=1～m]0.1
＋∑[n=1～m](9*0.1^n)}
=lim[m→∞]{0.1^m
＋∑[n=1～m](9*0.1^n)}
･ ･
=(1ｰ0.9)+0.9
=1