Question

proof LIM nto∞ 0.99...9=1？

Answer 1

are you asking why
.99999999999999999999... = 1?

Answer 2

let .99999999999... =x

10x= 9.99999999999999...
x=9.999999999999999999...

10x-x=9
9x=9
x=1

1=.999999999999999999999...

Answer 3

\[\lim_{n \rightarrow ?\infty}n \sqrt{n ^{2}-n} =\frac{ 1 }{ 2 }\]

Answer 4

put y=1/n
when n->infinity, y->0
replace all n by 1/y

Answer 5

there are lot's of reasons ... watch this out
http://www.youtube.com/watch?v=TINfzxSnnIE

Answer 6

and check this out
http://math.stackexchange.com/questions/11/does-99999-1