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## Main Question or Discussion Point

Pleas Answer the POll and dont close the thread as my project is due very very soon

- Thread starter chickenguy
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Pleas Answer the POll and dont close the thread as my project is due very very soon

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cepheid

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Integral

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One can show that this limit is 9/10 + 9/100 + 9/1000 ... using Analysis, and a proof really isn't all that hard (we all believe it intuitively anyway); a reference can be found in any of the Analysis texts referenced at the end of this message. Then all we have left to do is show that this sum really does equal 1:

Proof: 0.9999... = Sum 9/10^n

(n=1 -> Infinity)

= lim sum 9/10^n

(m -> Infinity) (n=1 -> m)

= lim .9(1-10^-(m+1))/(1-1/10)

(m -> Infinity)

= lim .9(1-10^-(m+1))/(9/10)

(m -> Infinity)

= .9/(9/10)

= 1

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