It depends on the series.
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The sum of the series a + ar + ar2 + ... is a/(1 - r) for |r| < 1
It's a geometric progression with the initial term 1/2 and common ratio 1/2. The infinite sum of the series is 1.
Yes, the sum of infinite ones equal the sum of infinite twos.
The absolute value of the common ratio is less than 1.
1/8