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The coefficient of x^(n) in (1+x+(x^(2))...

The coefficient of `x^(n)` in `(1+x+(x^(2))/(2!) + (x^(3))/(3!) +"….." + (x^(n))/(n!))^(3)` is

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. The sum of the GP (x+y)/(x-y), 1, (x-y)/(x+y),.....

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  2. Statement 1: In the expansion of (1+x)^(41)(1-x+x^2)^(40), the coeffic...

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  3. The coefficient of x^(n) in (1+x+(x^(2))/(2!) + (x^(3))/(3!) +"….." + ...

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  4. Evaluate the following .^3C2

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  5. Evaluate .^5C2

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  6. The value of sum(r=0)^(10)r""^(10)C(r)3^(r)(-2)^(10-r) is (a) 20 (b) 1...

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  7. Find n if n P1=2

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  8. Evaluate .^5P2

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  9. The value of (.^(n)C(0))/(n)+(.^(n)C(1))/(n+1)+(.^(n)C(2))/(n+2)+"..."...

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  10. The value of .^(20)C(0)+.^(20)C(1)+.^(20)C(2)+.^(20)C(3)+.^(20)C(4)+.^...

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  11. If (3+x^(2008)+x^(2009))^(2010)=a0+a1x^2+....+anx^n, a0-1/2 a1-1/2 a2+...

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  12. Find the seventh term of the G.P: 1, √3, 3, 3 √3, …..

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  13. Find the 10th term of the G.P. : 12, 4, 1 1/3,....

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  14. If (1+x)^(n) = C(0) +C(1)x+C(2)x^(2) + "….." + C(n)x^(n), then C(0)C(2...

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  15. The value of (lim)(n->oo)sum(r=1)^(n)(sum(t=0)^(r-1)1/(5^n).^n Cr.^r C...

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  16. If n gt 2, then prove that C(1)(a-1) - C(2) xx (a-2) + "….." + (-1)^(...

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  17. Find the nth term of the series: 1, 2, 4, 8, ……

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  18. The remainder, if 1+2+2^2+2^3+....+2^1999 in divided by 5 is

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  19. Largest real value for x such that underset(k=0)overset(4)sum((3^(4-k)...

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  20. If in the expansion of (a-2b)^(n), the sum of 5^(th) and 6^(th) terms ...

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