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If C(r) stands for ""^(n)C(r), then the ...

If `C_(r)` stands for `""^(n)C_(r)`, then the sum of the series `(2((n)/(2))!((n)/(2))!)/(n!)[C_(0)^(2)-2C_(1)^(2)+3C_(2)^(2)-...+(-1)^(n)(n+1)C_(n)^(2)]`, where n is an even positive integers, is:

A

0

B

`(-1)^(n/2)*(n+1)`

C

`(-1)^(n)*(n+1)`

D

`(-1)^n*n`

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A DAS GUPTA-Binomial Theorem for Positive Integrel Index-Exercise
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  2. The sum of ""^21C0+""^21C1+""^21C2+...+""^21C10 is equal to .

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  3. The coefficient of x^(n) y^(n) in the expansion of [(1 + x)(1+y) (x...

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  4. The number of terms in the expansion of (1+2x+x^2)^n is :

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  5. The number of terms in the expansion of (1+7sqrt(2x))^9+(1-7sqrt(2x))^...

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  6. In the expansion of (x^(3) - (1)/(x^(2)))^(15) , the constant term,i...

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  7. The largest coefficient in the expansion of (1+x)^24 is

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  8. 3^(51) when divided by 8 leaves the remainder 2 2. 6 3. 3 4. 5 5. 1

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  9. The sum of the series ""^20C0+""^20C1+""^20C2+...+""^20C9 is =

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  10. The sum of the last eight coefficients in the expansion of (1 + x)^16 ...

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  11. If C(r) stands for ""^(n)C(r), then the sum of the series (2((n)/(2))!...

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  12. If pa n dq are ositive, then prove that the coefficients of x^pa n dx^...

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  13. The number of dissimilar terms in the expansion of (a+2b+3c)^8 is

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  14. In the expansion of (1+x)^(2m)(x/(1-x))^(-2m) the term independent of ...

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  15. State true or false : The integral part of (8+3sqrt7)^20 is odd.

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  16. State true or false : In the expansion of (x^2/y+y^2/x)^15 there is no...

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  17. State true or false: In the expansion of (1+2x+x^2)^9 there is exactly...

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  18. State true or false : In the expansion of (x+1/x)^13 every term is a f...

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  19. State true or false : If f(x)=(x+1/x)^(2n)+(x-1/x)^(2n) the f(x) is a ...

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  20. State whether the statements are true or false : ""^16C0-""^16C1+""^16...

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