Question

0.999..=1 prove this question

Answer 1

x=0.9999...
10x =9.9999...
10x -x = 9.9999... - 0.9999
9x = 9
x = 9/9 = 1 = RHS
Hence proved

Answer 2

Initially we have 0.9999....

$x = 0.9999....$ -------------------1

$10x = 9.9999....$ ---------------2

$9x=9$                  (substracting 1 from 2)

$x=1$

∴ $0.999..=1$ .

QED