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If a(n) = sum(r=0)^(n) (1)/(""^(n)C(r))...

If ` a_(n) = sum_(r=0)^(n) (1)/(""^(n)C_(r)) ` , find the
value of ` sum_(r=0)^(n) (r)/(""^(n)C_(r))`

A

nk

B

`(nk)/(2)`

C

`(n-1)k`

D

`(nk)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
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AAKASH INSTITUTE ENGLISH-BINOMIAL THEOREM-Assignment (section-B)
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  2. Let (1+x^2)^2(1+x)^n=sum(k=0)^(n+4)ak x^k. If a1, a2 and a3 are in ari...

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  3. The coefficient of x^1007 in the expansion (1+x)^(2006)+x(1+x)^(2005)+...

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  4. underset(r=0)overset(n)(sum)(-1)^(r).^(n)C(r)[(1)/(2^(r))+(3^(r))/(2^(...

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  5. In the expansion of (x +a)^(n) the sum of even terms is E and that ...

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

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  7. The coefficient fo x^(3) y^(4) x^(5) in the expansion of (xy + yz +...

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  8. In the expansion of (3x+2y-z)^(8), the coefficients of x^(2)y^(3)z^(3)...

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  9. If n is ann integer greater than 1, then a-^(n)C(1)(a-1)+.^(n)C(2)(a...

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  10. (C(0))/(1)+(C(1))/(2)+(C(2))/(3)+ . . . .+(C(100))/(101) equals

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  11. 2C0+2^2/2 C1+2^3/3 C2+.............+2^11/11 C10 =?

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  12. The coefficient of x^(n) in the polynomial (x+""^(2n+1)C(0))(X+""^(2n+...

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  13. If C(r) stands for .^(n)C(r)=(n!)/(r!n-r!) and underset(r=1)overset(n)...

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  14. If a(n) = sum(r=0)^(n) (1)/(""^(n)C(r)) , find the value of sum(...

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  15. If x + y = 1, prove that underset(r=0)overset(n)sum r.^(n)C(r) x^(r ) ...

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  16. underset(r=1)overset(n)(sum)r(.^(n)C(r)-.^(n)C(r-1)) is equal to

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  17. The expression ""^(n)C(r)+4.""^(n)C(r-1)+6.""^(n)C(r-2)+4.""^(n)C(r-...

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  18. If underset(k=0)overset(n)(sum)(k^(2)+k+1)k! =(2007).2007!, then value...

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  19. Let R=(5sqrt(5)+11)^(2n+1)a n df=R-[R]w h e r e[] denotes the greatest...

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  20. Find the coefficient of x^4 in the expansion of (1+x+x^2+x^3)^(11)dot

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