The sum of the series $^{20} C_{0} +^{20} C_{1} +^{20} C_{2} + . . . +^{20} C_{10}$ is

2^{20}

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2^{19}

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2^{19} + \frac{1}{2} .^{20} C_{10}

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2^{19} - \frac{1}{2} .^{20} C_{10}

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Solution

The correct option is C $2^{19} + \frac{1}{2} .^{20} C_{10}$
$(1 + x)^{20} =^{20} C_{0} +^{20} C_{1} x + . . . . . . . . +^{20} C_{20} x^{20}$
$2^{20} =^{20} C_{0} +^{20} C_{1} + . . . . +^{20} C_{10} +^{20} C_{11} + . . . . . . . . +^{20} C_{20}$
$2^{19} =^{20} C_{0} + . . . . . +^{20} C_{9} +^{20} C_{10} - {\frac{1}{2}}^{20} C_{10}$
$∴^{20} C_{0} + \to +^{20} C_{10} = 2^{19} + {\frac{1}{2}}^{20} C_{10}$

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Similar questions

^{20} C_{0} -^{20} C_{1} +^{20} C_{2} -^{20} C_{3} + . . . . . - . . . . . +^{20} C_{10}

^{20} C_{0} -^{20} C_{1} +^{20} C_{2} -^{20} C_{3} + . . . . . - . . . . . . +^{20} C_{10}

{^{20} C}_{0} - {^{20} C}_{1} + {^{20} C}_{2} - {^{20} C}_{3} + . . . . + {^{20} C}_{10}

^{20} C_{0} -^{20} C_{1} +^{20} C_{2} -^{20} C_{3} + . . . +^{20} C_{10} =

\frac{C_{0}}{1} + \frac{C_{1}}{2} + \frac{C_{2}}{3} + . . . . . . + \frac{C_{10}}{11} =

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