help with a sum | Mathematics | Page 1

misty seal Mar 1, 2025, 2:30 PM

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i need to prove why this is a true statement!

merry umbraBOT Mar 1, 2025, 2:30 PM

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late oak Mar 1, 2025, 2:47 PM

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misty seal i need to prove why this is a true statement!

Basically, $\ 0.9 + 0.09 + ... = 0.999... = 1$

glass harnessBOT Mar 1, 2025, 2:47 PM

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UnexpectedTaco

late oak Mar 1, 2025, 2:48 PM

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The most common method to go about this is as follows:
$\$ let $x = 0.999... \ 10x = 9.999... \ 10x - x = 9.999... - 0.999... = 9 \ 9x = 9 \ x = 1$

glass harnessBOT Mar 1, 2025, 2:48 PM

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UnexpectedTaco

late oak Mar 1, 2025, 2:51 PM

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Although this isn't too rigorous. $\$
More ways:
$\ \frac{1}{3} = 0.333... \ \ 1 = 0.999... \ \$
Another way to go about this is to look at the number line. There is no number you can imagine between 0.999... and 1!

glass harnessBOT Mar 1, 2025, 2:51 PM

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UnexpectedTaco

misty seal Mar 1, 2025, 3:14 PM

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thanks!

late oak Mar 1, 2025, 7:23 PM

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No problem.

merry umbraBOT Mar 2, 2025, 2:57 AM

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late oak No problem.

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merry umbraBOT Mar 2, 2025, 2:57 AM

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misty seal thanks!

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misty seal Mar 2, 2025, 2:15 PM

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.close

#help with a sum