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If a(K)=(1)/(K(K+1)) for K=1, 2, 3....n,...

If `a_(K)=(1)/(K(K+1))` for `K=1, 2, 3....n`, then `(sum_(K=1)^(n)a_(K))^(2)=`

A

`(n)/(n+1)`

B

`(n^(2))/((n+1)^(2))`

C

`(n^(4))/((n+1)^(4))`

D

`(n^(6))/((n+1)^(6))`

Text Solution

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The correct Answer is:
B
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AAKASH SERIES-PARTIAL FRACTIONS-EXERCISE - II
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  2. If (1)/((x-a)(x^(2)+b))=(A)/(x-a)+(Bx+C)/(x^(2)+b) then (1)/((x-a)(x^(...

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  3. If (x-4)/(x^(2)-5x+6) can be expanded in the ascending powers of x, th...

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  4. The coefficient of x^(n) in (1)/((1-2x)(1-3x)) is

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  5. The coefficient of x^(n) in (x+1)/((x-1)^(2)(x-2)) is

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  6. The number of partial fractions of (x^(3)-3x^(2)+3x)/((x-1)^(5)) is

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  7. The number of partial fractions of (2)/(x^(4)+x^(2)+1) is

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  8. If a(K)=(1)/(K(K+1)) for K=1, 2, 3....n, then (sum(K=1)^(n)a(K))^(2)=

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  9. For |x| lt 1/5, the coefficient of x^(3) in the expansion of (1)/((1-...

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  10. (3x^(2)+x+1)/(x-1)^(4)=a/(x-1)+b/(x-1)^(2)+c/(x-1)^(3)+d/(x-1)^(4) rAr...

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  11. Statement-I : If (x^(2)+3x+1)/(x^(2)+2x+1)=A+(B)/(x+1)+(C)/((x+1)^(2...

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  12. Statement-I : If (3x+4)/((x+1)^(2)(x-1))=(A)/(x-1)+(B)/(x+1)+(C)/((x...

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

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  14. (2x^(4)+3x^(2)+1)/((x^(2)+1)^(4))=(A)/((x^(2)+1))+(B)/((x^(2)+1^(2)))+...

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  15. A : If (5x+1)/((x+2)(x-1))=A/(X+2)+B/(x-1) " then "A=3, B=2. R : (px...

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  16. Assertion (A) : The remainder of x^(3)+2x^(2)-5x-3 which is divided by...

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  17. Assertion (A) : If (1)/(x^(3)(x+2))=A/x + B/x^(2) +C/x^(3) + D/(x+2) t...

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  18. If the expansion in powers of x of the function (1)/((1-ax)(1-bx)) is ...

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  19. (1)/(x(x+1)(x+2).....(x+n))=(A(0))/(x)+(A(1))/(x+1)+...+(A(n))/(x+n) r...

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  20. If 1/(x^(4)+x^(2)+1)=(Ax+B)/(x^(2)+x+1)+(Cx+D)/(x^(2)-x+1) " then "C+D...

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