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Sum of Coefficients of All Terms

The value of ...

Question

The value of $^{15} C_{0} +^{15} C_{1} +^{15} C_{2} + \dots +^{15} C_{7}$ is

A

2^{14}

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B

2^{15}

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C

2^{13}

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D

2^{7}

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Solution

The correct option is A $2^{14}$
Let $S =^{15} C_{0} +^{15} C_{1} +^{15} C_{2} + \dots +^{15} C_{7}$
We know that,
$^{15} C_{0} +^{15} C_{1} +^{15} C_{2} + \dots +^{15} C_{15} = 2^{15} \Rightarrow S +^{15} C_{8} + \dots +^{15} C_{15} = 2^{15} \Rightarrow 2 S = 2^{15} (∵^{15} C_{r} =^{15} C_{15 - r}) ∴ S = 2^{14}$

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Sum of Coefficients of All Terms

Standard XII Mathematics

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