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Question

The sum Sn=nk=0(1)K.3nCk, is

A
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B
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C
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D
None of these
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Solution

The correct option is D
Sn=3nC03nC1+3nC2+.....+(1)n.3nCnBut3nC0=3n1C03nC1=3n1C03n1C13nC2=3n1C1+3n1C23nC3=3n1C23n1C3............................(1)n.3nCn=(1)n.3n1C1+(1)n.3n1Cn
On adding we get Sn=(1)n.3n1Cn

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