Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you use a geometric series to prove that $0.999…=1$ ?

1 Answer

Sep 12, 2014

We can write
#0.999...=9/10+9/100+9/1000+cdots# #=9/10+9/10(1/10)+9/10(1/10)^2+cdots=sum_{n=0}^infty 9/10(1/10)^n#, which is a geometric series with #a=9/10 $and$ r=1/10#.

So, the sum is
$a/{1-r}={9/10}/{1-1/10}=1$

Related questions

See all questions in Geometric Series

Impact of this question

8179 views around the world

You can reuse this answer
Creative Commons License