What is the sum of $1 - 1/2 + 1/4 - 1/8 + 1/16 - 1/32\dots$? [closed]

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I couldn't find out the exact value of this operation.

$$1 - 1/2 + 1/4 - 1/8 + 1/16 - 1/32 \dots$$

You go 1 units right on the number line, half of it to the left, half of the previous one to the right... But I don't know where exactly it ends up when we do this infinite times.

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2 Answers

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Hint: $$ \sum_{n=0}^\infty x^n=\frac{1}{1-x} $$ when $|x|<1$.

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Hint:

$$ \begin{align} S &= \color{blue}{1 - 1/2 + 1/4 - 1/8 + 1/16 - 1/32 \dots} \\ 4S &= 4 - 2 + \color{blue}{1 - 1/2+1/4-1/8+\ldots} = 2 + S \end{align} $$

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