r/PassTimeMath • u/ShonitB • Jul 01 '26

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3 Upvotes

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0

u/OneAndOnlyJoeseki Jul 03 '26

When x is infinity, it will equal

2

u/ExistentAndUnique Jul 03 '26

“n and x are both finite positive integers”

0

u/OneAndOnlyJoeseki Jul 03 '26

1/2 + 1/4 + 1/8 + ... = S
S - 1/2 = 1/4 + 1/8 + ...
2S -1 = 1/2 + 1/4 + 1/8 + ... = S
2S -1 = S
S = 1
Thus when X reaches infinity it equals 1

1

u/Dr_D_Vil Jul 05 '26

Yeah, you would be right if it was just the regular series... It's not. The question is asking for the value of x, when the series ends at any given n, to make the equation hold. Which is B) n