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# Infinity

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)

Note by Lokesh Sharma
4 years, 5 months ago

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I posted this before · 4 years, 5 months ago