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Question

If Cr=Cr2n+1 then, C0-C12+C22+....+(-1)C22n+12n+1 is equal to?


A

Cn2n+1-C2n+12n+12

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B

Cn2n

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C

1nCn2n

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D

0

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Solution

The correct option is D

0


Find the value of C0-C12+C22+....+(-1)C22n+12n+1:

Given, Cr=Cr2n+1

As we know,

(1-x)n=C0-C1x+C2x2-.....+Cnxn

Put x=1

0=C0-C1+C2-.....+Cn

Now,

(1-x)n(1-x)n=C0-C1x+C2x2-.....+CnxnC0-C1x+C2x2-.....+Cnxn

1-x2n=C0-C12x+C22x2-.....+Cn2xn+-12n+1C22n+1

Again put x=1

(C0-C12+C22-.....+Cn2+-12n+1C22n+1)=0

Hence, Option ‘D’ is Correct.


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