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Question

If Dr=2r12.3r14.5r1αβγ2n13n15n1∣ ∣ ∣,then the value of nr=1 Dr is



A

0

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B

αβγ

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C

α+β+γ

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D

α2n+β3n+γ4n

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Solution

The correct option is A

0


nr=1 2r1=1+2+22+...+2n1=2n121=2n1nr=1 2.3r1=2(3n1)31=3n1nr=1 4.5r1=4(5n1)51=5n1nr=1 Dr=2n13n15n1αβγ2n13n15n1∣ ∣ ∣=0


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