Sum to infinity

1/10 + 2/10^2 + 3/10^3 + 4/10^4 + 5/10^5 + ...

= (1/10 + 1/10^2 + 1/10^3 + 1/10^4 + 1/10^5 + ...) +
(1/10^2 + 1/10^3 + 1/10^4 + 1/10^5 + ...) +
(1/10^3 + 1/10^4 + 1/10^5 + ...) +
(1/10^4 + 1/10^5 + ...)

= (1/10)/(1 - 1/10) + (1/10^2)/(1 - 1/10) + (1/10^3)/(1 - 1/10) + ...

= (10/9)[1/10 + 1/10^2 + 1/10^3 + ...]

= (10/9)[(1/10)/(1 - 1/10)]

= 1/9[10/9]

= 10/81

So, the answer is B.

圖片參考：http://i826.photobucket.com/albums/zz190/fai109/47.jpg?t=1271227045

The ans. is B .

A=1/10 + 2/10^2 + 3/10^3 + 4/10^4 + 5/10^5 ....
A/10= 1/10^2+ 2/10^3 +.3/10^4 +4/10^5+....
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9A/10=1/10+1/10^2+1/10^3+.....=(1/10)/[1-(1/10)]=1/9
A=10/81