I wasnt sure which math forum to ask this in so im putting it here, apologies if its supposed to be elsewhere.(adsbygoogle = window.adsbygoogle || []).push({});

Anyway, my question has to do with an infinite sum.

Suppose we have a series:

1+2+4+8+16+32+...

each term in the series is double the previous term starting with 1

if we multiply this by the number 1 it will remain the same

1+2+4+8+16+32+... = 1(1+2+4+8+16+32+...)

also (2-1) = 1

so we can say

1+2+4+8+16+32+... = (2-1)(1+2+4+8+16+32+...)

if we expand the RHS we get

1+2+4+8+16+32+... = (2+4+8+16+32+64+...) - (1+2+4+8+16+32+...)

1+2+4+8+16+32+... = (2+4+8+16+32+64+...) + (-1-2-4-8-16-32-...)

the first part of the RHS has a set of all positive even numbers and the 2nd part of the set has a set of all negative even numbers

all the even numbers will subtract to 0 and i'm left with

1+2+4+8+16+32+... = -1

what have I done wrong? I can't figure what and where the error is.

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# Infinite Sum Question

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