0.9999...=∞(0.9)(0.1)^n-1= 0.9/1-0.1=1,

∑

n=1

using the geometric series. By the same method, compute the exact

value of the following periodic innite decimal expression as a rational number: 0:89898989

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- November 19th 2013, 12:28 PMDfaulk044sequences and series
0.9999...=∞(0.9)(0.1)^n-1= 0.9/1-0.1=1,

∑

n=1

using the geometric series. By the same method, compute the exact

value of the following periodic innite decimal expression as a rational number: 0:89898989

- November 19th 2013, 12:38 PMPlatoRe: sequences and series
- November 19th 2013, 12:43 PMebainesRe: sequences and series
First let me rewrite what I think you tried to convey:

If you do long division of 1-0.1 into 0.9 you get the infinite series .9 + .01 + .009 + ....; Hence 0.99999... = 1.

For the number 0.898989.. you have:

.

To show this do the long division of 1 - .01 into 0.89.