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""^(15)C(0)=...

`""^(15)C_(0)=`

A

15

B

-15

C

0

D

51

Text Solution

Verified by Experts

The correct Answer is:
C
As we know that `.^(n)C_(0)-.^(n)C_(1)^(2) + .^(n)C_(3)^(2)+"…."+(-1)^(n).^(n)C_(n)^(2) = 0` .
(if n is odd) and in the question `n = 15` (odd). Hence, sum of given series is 0.
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CENGAGE-BINOMIAL THEOREM-Exercise (Single)
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  6. The value of sum(r=0)^(40) r""^(40)C(r)""^(30)C(r) is

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  9. The value of sum(r=0)^(50)(-1)^r(^(50)Cr)/(r+2) is equal to 1/(50xx51)...

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  10. sum(r=0)^(300)ar x^r=(1+x+x^2+x^3)^(100)dot If a=sum(r=0)^(300)ar ,t ...

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  11. sum(r=0)^(300)ar x^r=(1+x+x^2+x^3)^(100)dot If a=sum(r=0)^(300)ar ,t ...

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  12. The value of sum(r=0)^(20)r(20-r)(^(20)Cr)^2 is equal to 400^(39)C(20)...

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  15. In the expansion of [(1+x)//(1-x)]^2, the coefficient of x^n will be 4...

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