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The sum of the series ""^20 C0-""^20 C...

The sum of the series ` ""^20 C_0-""^20 C_1+""^20C_2-""^20C_3+...-...+""^20C_10` is:

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To find the sum of the series \[ S = \binom{20}{0} - \binom{20}{1} + \binom{20}{2} - \binom{20}{3} + \ldots - \binom{20}{10}, \] we can use the Binomial Theorem. ...
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