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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)) =

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VMC MODULES ENGLISH-BINOMIAL THEOREM-JEE Archive
  1. The value of ((30), (0))((30), (10))-((30), (1))((30),( 11)) +(30 2)(3...

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  2. If ^n-1Cr=(k^2-3)^n C(r+1),t h e nk in (-oo,-2] b. [2,oo) c. [-sqrt...

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  3. The sum sum(i=0)^m ((10)c,(i))((20),(m-1)), where ((p),(q))=0 if p ...

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  4. ""^(n)C(r+1)+^(n)C(r-1)+2.""^(n)C(r)=

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  5. If an=sum(r=0)^n1/(^n Cr) , then sum(r=0)^n r/(^n Cr) equals (n-1)an b...

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  6. about to only mathematics

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  7. Prove that the sum of the coefficients in the expansion of (1 + x ...

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  8. If n and k are positive integers, show that 2^k(nC 0)(n k)-2^(k-1)(nC1...

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

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

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  11. Let n be a positive integer and (1+x+x^2)^n=a0+a1x+ . . . . +a(2n)x^(2...

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  12. Prove that C0-2^2C1+3^2C2-4^2C3++(-1)^n(n+1)^2xxCn=0w h e r eCr=^n Cr ...

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  14. Prove that C(1)^(2)-2*C(2)^(2)+3*C(3)^(2)-…-2n*C(2n)^(2)=(-1)^(n)n*C(n...

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  15. (.^(n)C(0))^(2)+(.^(n)C(1))^(2)+(.^(n)C(2))^(2)+ . . .+(.^(n)C(n))^(2)...

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  16. The coefficient of x^(18) in the product (1+x)(1-x)^(10)(1+x+x^(2))^(9...

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  17. The term independent of x in the expansion of (1/60-(x^(8))/81).(2x^(...

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  18. Value of r for which expression ^20Cr ^20C0+^20C(r-1) ^20C1+^20C(r-2)^...

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  19. If the fractional part of the number (2^(403))/(15) is (k)/(15) then k...

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  20. Let X = (.^(10)C(1))^(2) + 2(.^(10)C(2))^(2) + 3(.^(10)C(3))^(2) + "……...

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