What is the sum of the infinite series 1/2 + 1/4 + 1/8 +? Is the sum equal to 2?

 What is the sum of the infinite series 1/2 + 1/4 + 1/8 +? Is the sum equal to 2?

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The series you're describing is a geometric series with a common ratio of 1/2.

The sum of an infinite geometric series $𝑎+𝑎𝑟+𝑎{𝑟}^2+𝑎{𝑟}^3+\dots$ where $\mathrm{\mid }𝑟\mathrm{\mid }<1$ is given by the formula:

$\text{Sum}=\frac{𝑎}{1-𝑟}$

In your series, $𝑎=\frac{1}{2}$ and $𝑟=\frac{1}{2}$. So, substituting into the formula:

$\text{Sum}=\frac{\frac{1}{2}}{1-\frac{1}{2}}=\frac{\frac{1}{2}}{\frac{1}{2}}=1$

The sum of the infinite series $\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\dots$ is indeed equal to 1, not 2. It converges to 1, not 2.