How do I use a geometric series to prove that #0.999...=1#?

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Answer 1 · 2014-10-04T02:46:48

#0.999...#

by separating digits,

#=0.9+0.09+0.009+cdots#

by rewriting in the form of a geometric series,

#=9/10+9/10(1/10)+9/10(1/10)^2+cdots#

by the sum formula for a convergent geometric series,

#={9/10}/{1-1/10}=1#

I hope that this was helpful.