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Prove that (3!)/(2(n+3))=sum(r=0)^n(-1)^...

Prove that `(3!)/(2(n+3))=sum_(r=0)^n(-1)^r((^n C_r)/(^(r+3)C_r))`

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sum_(r = 0)^(n-1) (C_r)/(C_r + C_(r+1)) =

If n in N, then sum_(r=0)^(n) (-1)^(n) (""^(n)C_(r))/(""^(r+2)C_(r)) is equal to .

Prove that sum_(r=1)^n(-1)^(r-1)(1+1/2+1/3++1/r)^n C_r=1/n .

Prove that sum_(r=0)^ssum_(s=1)^n^n C_s^n C_r=3^n-1.

Prove that sum_(r=0)^n r(n-r)(^nC_ r)^2=n^2(^(2n-2)C_n)dot

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Prove that sum_(r=0)^n^n C_r3^r=4^n

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CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. In the expansion of (1+3x+2x^2)^6 , the coefficient of x^(11) is a. 14...

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  2. If n-1Cr=(k^2-3)^nC(r+1), then (a) (-oo,-2] (b) [2,oo) (c) [-sqrt3, s...

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  3. Prove that (3!)/(2(n+3))=sum(r=0)^n(-1)^r((^n Cr)/(^(r+3)Cr))

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  4. If an=sum(r=0)^n1/(nCr), then sum(r=0)^n r/(nCr) equals

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  5. The expression (x+((x^3-1)^(1/2))/2)^5+""(x-((x^3-1)^(1/2))/2)^5 is a ...

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  6. Find ((dy) /dx) of sin(costheta) is

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  7. In the binomial expansion of (a-b)^n,ngeq5, the sum of the 5th and 6t...

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  8. Coefficient of x^(11) in the expansion of (1+x^2)^4(1+x^3)^7(1+x^4)^(...

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  9. Given positive integers r gt 1, n gt 2 and that the coefficient of (3...

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  10. The coefficient of x^4 in (x//2-3//x^2)^10 is a.(405)/(256) b. (504)/(...

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  11. If Cr stands for nCr, then the sum of the series (2(n/2)!(n/2)!)/(n...

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  12. The sum underset(m)overset(i=0)sum ({:(10),(i):})({:(20),(m-i):}), (wh...

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  13. The coefficient of X^24in the expansion of (1+X^2 )^12(1+X^12)(1+X^24)

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  14. The term independent of a in the expansion of (1+sqrta+ 1/(sqrta-1))^-...

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  15. The coefficient of x^(53) in the expansion sum(m=0)^(100)^100Cm(x-3)^(...

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  16. The coefficient of the term independent of x in the exampansion of ((x...

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  17. In the expansion of (1+x+x^3+x^4)^10, the coefficient of x^4 is ^40C4 ...

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  18. If coefficient of a^2 b^3 c^4 in(a+b+c)^m (where n in N) is L(L != 0)...

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  19. The last two digits of the number 3^(400) are: (A) 81 (B) 43 (C) ...

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  20. The expression (sqrt(2x^2+1)+sqrt(2x^2-1))^6 + (2/(sqrt(2x^2+1)+sqrt(2...

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