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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_3))`

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. In the expansion of (1+3x+2x^(2))^(6), find the coefficient of x^(11).

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

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  3. Prove that (3!)/(2(n+3))=sum(r=0)^n(-1)^r((n Cr)/((r+3)C3))

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  4. Find the 5th term of the GP. 5/2, 1, .....

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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(cosx) 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)^12 i...

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  9. Give the integers rgt1 , ngt2 and c0-efficients of (3r)^th and (r+2)^(...

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  10. Find the coefficient of x^4 in the expansion of (x//2-3//x^2)^(10)dot

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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. If the sum 1+2+2^2+......+2^(n-1)is 255, then find the number of ter...

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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. Find the sum of the GP 1+3+9+27+........ 12terms

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

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  16. The coefficient of the term independent of x in the expansion of [((x+...

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

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

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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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