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Evaluate sum(i=0)^(n)sum(j=0)^(n) ""^(n)...

Evaluate `sum_(i=0)^(n)sum_(j=0)^(n) ""^(n)C_(j) *""^(j)C_(i), ile j ` .

A

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

B

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

C

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

D

`n*2^(n)`

Text Solution

Verified by Experts

The correct Answer is:
A
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VMC MODULES ENGLISH-BINOMIAL THEOREM-LEVEL 2
  1. If .^(47)C(4)+underset(r=1)overset(5)(sum).^(52-r)C(3) is equal to

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  2. sum(r=0)^m .^(n+r)Cn is equal to

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  3. Evaluate sum(i=0)^(n)sum(j=0)^(n) ""^(n)C(j) *""^(j)C(i), ile j .

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  4. sum(r=0)^(n)((r+2)/(r+1))*""^(n)C(r) is equal to :

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  5. The expression (""^(10)C(0))^(2)-(""^(10)C(1))^(2)+(""^(10)C(2))^(2)...

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  6. If C(0),C(1), C(2),...,C(n) denote the cefficients in the expansion...

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  7. If (1 + x)^(n) = C(0) + C(1) x + C(2) x^(2) +…+ C(n) x^(n) , find the...

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  8. If (1 + x)^(n) = C(0) + C(1) x + C(2) x^(2) +…+ C(n) x^(n) , find the...

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  9. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+….+C(n)x^(n), then the value of sums...

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  10. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+….+C(n)x^(n), then the value of sums...

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  11. Find the value of underset(0leiltjlen)(sumsum)(.^(n)C(i)+.^(n)C(j)).

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  12. If n is a positive integer and C(k)=""^(n)C(k), then the value of sum(...

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  13. If C(0),C(1),C(2),…,C(n) are the binomial coefficients in the expansio...

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  14. Find the sum of 1/(1!(n-1)!)+1/(3!(n-3)!)+1/(5!(n-5)!)+ ...,

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  15. If (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+….+a(2n)x^(2n) where a(0), a(...

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  16. For any positive integer (m,n) (with ngeqm), Let ((n),(m)) =.^nCm Prov...

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  17. Prove that ""^(n)C(3)+""^(n)C(7) + ""^(n)C(11) + ...= 1/2{2^(n-1) -...

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  18. If n in N, then sum(r=0)^(n) (-1)^(n) (""^(n)C(r))/(""^(r+2)C(r)) is ...

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  19. The value of ((50),(0))((50),(1))+((50),(1))((50),(2)) + ...+ ((50),(...

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  20. The value of sum(r=0)^(n) sum(p=0)^(r) ""^(n)C(r) . ""^(r)C(p) is...

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