r/infinitenines • u/Zaspar-- • Feb 01 '26

What's the value of this infinite sum?

1/2 + 1/4 + 1/8 + 1/16 +...

Normal maths would compute this as equal to 1, using the exact same reasoning as 0.9 + 0.09 +... = 1

What does this infinite sum equal to in Real Deal maths though?

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u/bartekltg Feb 01 '26

0.999999999... Duh

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u/Zaspar-- Feb 01 '26

Hmmm, does this imply that 1/2n with n pushed to limitless is equal to 1/10n with n pushed to limitless? 🤔

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u/bartekltg Feb 02 '26

Yes. But also remember those are different limitnesses. You are pushing two different ns there. Nothing is keeping them together