Infinity

Main post link -> http://en.wikipedia.org/wiki/1%2B2%2B4%2B8%2B%E2%8B%AF

What is this supposed to mean -

"In mathematics, 1 + 2 + 4 + 8 + … is the infinite series whose terms are the successive powers of two. As a geometric series, it is characterized by its first term, 1, and its common ratio, 2. As a series of real numbers it diverges to infinity, so in the usual sense it has no sum. In a much broader sense, the series is associated with another value besides ∞, namely −1." -Wikipedia

How could sum of numbers be associated with two unequal numbers. Doesn't it violate any mathematical laws? Doesn't it create a difficult mathematical situation in which we might say -1=∞ and how can we really interpret this result? For those who are wondering how 1+2+4+8+.... = -1. Notice this could be written as 1+2(1+2+4+...)=1+2+4+8+16+.... Lets say 1+2+4+8+16... = s. Now we get 1+2s=s which implies s = -1. (See the link)

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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Comments

I posted this before

Zi Song Yeoh - 8 years, 2 months ago

OH I didn't knew that. Can you give the link?

Lokesh Sharma - 8 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$