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Show that (n !)/(x(x+1)(x+2)...(x+n))=("...

Show that `(n !)/(x(x+1)(x+2)...(x+n))=(""^(n)C_(0))/(x)-(""^(n)C_(1))/(x+1) + (""^(n)C_(2))/(x+2)-(""^(n)C_(3))/(x+3) + ...+ ((-1)^(n)""^(n)C_(n))/(x+n)`.

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Prove that (""^(2n)C_(0))^(2)-(""^(2n)C_(1))^(2)+(""^(2n)C_(2))-(""^(2n)C_(3))^(2)+......+(""^(2n)C_(2n))^(2)=(-1)^(n)(""^(2n)C_(n))^2.

""^(2n)C_(n+1)+2. ""^(2n)C_(n) + ""^(2n) C_(n-1) =

If ""^(n)C_(r) +""^(n) C_(r+1)= ""^((n+1)) C_(x) then x=

""^n C_0- ^n C_1 + ^n C_2.....(-1)^n ""^n C_n=

C_0-(C_1)/(2)+(C_2)/(3)-…...+(-1)^n (C_n)/(n+1)=

Prove that 1-""^(n)C_(1) (1+x)/(1+n x)+""^(n)C_(2) (1+2x)/((1+n x)^(2)) ""^(n)C_(3) (1+3x)/((1+n x)^(3)) +….(n+1) terms = 0

Match the following {:("List-I","List-II"),((I)""^(n)C_(r+1)+2""^(n)C_(r)+""^(n)C_(r-1),(a)""^((n+2))C_(r+1)),((II)""^((n+1))C_(3)-""^(n-1)C_(3),(b)(n-1)^(2)),((III)""^(2n)C_(2)-2""^(n)C_(2),(c)n^(2)),(,(d)""^(n+1)C_(r+1)):} The correct match is

AAKASH SERIES-PARTIAL FRACTIONS-PRACTICE EXERCISE
  1. Show that (n !)/(x(x+1)(x+2)...(x+n))=(""^(n)C(0))/(x)-(""^(n)C(1))/(x...

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  2. The remainder obtained when the polynomial x^(4)-3x^(3)+9x^(2)-27x+81 ...

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  3. If the remainder of the polynomial f(x) when divided by x+1 and x-1 ar...

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  4. If (3x+4)/(x^(2)-3x+2)=A/(x-2)-B/(x-1) then (A, B) =

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  5. If (1-x+6x^(2))/(x-x^(3))=A/x +(B)/(1-x)+(C)/(1+x), then A=

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  6. If (x^(2)+5)/(x^(2)+2)^(2)=1/(x^(2)+2)+k/(x^(2)+2)^(2) " then " k=

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  7. If (x+1)/((x-a)(x-3))=2/(x-a)+b/(x-3), " then "(a, b)=

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  8. (2x-1)/((x-1)(2x+3))=1/(5(x-1))-k/(5(2x+3)), then k =

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  9. If (x^(2)-10x+13)/((x-1)(x^(2)-5x+6))=A/(x-1)+B/(x-2)+C/(x-3), then C ...

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  10. if (5x^(2) +2)/(x^(3)+x)=(A(1))/(x)+(A(2)x+A(3))/(x^(2)+1), then (A(...

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  11. If (x^(3))/((x-a)(x-b)(x-c))=1 +(A)/(x-a)+(B)/(x-b)+(C)/(x-c) then A=

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  12. If (x^(4))/((x-1)(x-2))=x^(2)+3x+7+(A)/(x-2)+(B)/(x-1) then A=

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  13. ((x+1))/((2x-1)(3x+1))=A/((2x-1))+B/((3x+1)) rArr 16A+9B=

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  14. If (x^(2)+1)/((x^(2)+2)(x^(2)+3))=(A)/(x^(2)+3)+(B)/(x^(2)+2) then (A,...

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  15. If (x^(2)+x+1)/(x^(2)+2x+1)=A+B/(x+1)+C/(x+1)^(2) then A - B =

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  16. If (x^(2)-5x+7)/(x-1)^(3)=A/(x-1)+B/(x-1)^(2)+C/(x-1)^(3) " then " A+B...

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  17. Resolve the following into partial fractions. (3x^(2)-8x^(2) + 10)/(...

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  18. If (2x^(2)+5)/((x+1)^(2)(x-3))=(A)/(x+1)+(B)/((x+1)^(2))+(C)(x-3) then...

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  19. The partial fractions of (1)/(x^(2)(x+2)) are

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  20. If (x^(4))/((x-1)(x-2)(x-3))= A.x+B. (1)/((x-1))+C (1)/((x-2))+D. (1)/...

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  21. If (2x^(2)+3x+4)/((x-1)(x^(2)+2))=A/(x-1)+(Bx+C)/(x^(2)+2), " then "B=

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