0.9 infinite loop = 1
To prove this point:
The method 1 is the simplest and clearest.
Let x = 0.99...;; Then10x = 9.99 ...; Then 10X-X=9 can get X= 1.
Similarly, 9.99...= 10
Method 2 introduces the concept of limit.
The concept of limit appears in high school mathematics.
0.9999……
=0.9+0.09+0.009+……
= 0.9 * (1+0.1+0.01+0.001+...) geometric series sum.
= 0.9 * (1-0.1n)/(1-0.1), and n tends to infinity.
=0.9* 1/0.9
= 1
Similarly, 9.99...= 10
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