The sum to the infinite geometric series is calculated using:
[tex]\mathbf{S_{\infty} = \frac{a}{1-r}}[/tex]
Where a represents the first term, and r represents the common ratio
Assume the first term of the series is 2, and the common ratio is 1/2.
The sum to infinite becomes
[tex]\mathbf{S_{\infty} = \frac{2}{1-1/2}}[/tex]
Simplify the denominator
[tex]\mathbf{S_{\infty} = \frac{2}{1/2}}[/tex]
Divide the fractions
[tex]\mathbf{S_{\infty} = 4}[/tex]
Hence, the sum to infinity is 4
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