Unformatted text preview: and more terms, the sum gets closer and closer to some ﬁxed value. That is, look at 1 2 = 1 2 3 4 = 1 2 + 1 4 7 8 = 1 2 + 1 4 + 1 8 15 16 = 1 2 + 1 4 + 1 8 + 1 16 and so on, and ask whether these values have a limit. It seems pretty clear that they do, namely 1. In fact, as we will see, it’s not hard to show that 1 2 + 1 4 + 1 8 + 1 16 + ··· + 1 2 i = 2 i1 2 i = 11 2 i 233...
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 Fall '07
 JonathanRogawski
 Math, Calculus, Sequences And Series, Limit of a sequence

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