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The sum of n terms of the series : (1)...

The sum of n terms of the series `:`
`(1)/( 1.2.3.4) + ( 1)/( 2.3.4.5) + ( 1) / ( 3.4.5.6.)+"......."` is `:`

A

`( n^(3) + 6)/( 18( n + 1) ( n + 2) ( n + 3))`

B

` (1)/( 18)- ( 1)/( 3( n + 1) ( n + 2))`

C

`(1)/( 66) - ( 1)/( 2(n+1) ( n + 2) ( n + 3))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
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MODERN PUBLICATION-SEQUENCES AND SERIES -MCQ ( Level-II)
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  2. If a(1) , a(2),"………",a(n) are n non-zero real numbers such that ( a(1)...

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  3. The sum of n terms of the series : (1)/( 1.2.3.4) + ( 1)/( 2.3.4.5) ...

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  4. If sum(r=1)^(prop) t(r ) = ( n (n +1) ( n + 2) ( n + 3))/( 8 ) , wher...

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  5. sum(i=1)^(n) sum(j=1)^(i)sum(k=1)^(j) 1 equals :

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  6. If log(x)a,a^(x//2) and log(b)x are in G.P., then x equals :

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  7. If x,y,z are in A.P. and tan^(-1)x , tan^(-1)y and tan^(-1) z are als...

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  8. If P,Q,R be the A.M., G.M., H.M. respectively between any two rational...

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  9. Let S = ( 8 ) /( 5) + ( 16)/( 65) +"...." + ( 128)/( 2^(18) + 1) , th...

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  11. Let alpha, beta be the roots of x^(2) -x + p = 0 and gamma , delta b...

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  12. If the sum of the first 2n terms of the A.P. 2,5,8,"……….." is equal to...

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  13. The first term of a G. P. is 1. The sum of the third and fifth terms i...

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  14. Suppose a,b,c are in A.P. and a^(2) , b^(2) , c^(2) are in G.P. If a ...

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  15. If sum of the roots of the quadratic equation ax^(2) + bx+c = 0 is equ...

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  16. If f(x) is a polynomial function of second degree. IF f(1) = f(-1) and...

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  17. The sum of first n terms of the series 1^(2) + 2.2^(2) +3^(2) + 2. 4...

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  18. If s= sum(n=0)^(oo) a^(n) , y = sum(n=0)^(oo) b^(n) , z= sum (n=0)^(oo...

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  19. If alpha, beta are roots of ax^(2) + bx + c =0 , a cancel(=) 0 and alp...

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  20. Let a(1) , a(2) , a(3) , "……………" be terms of an A.P. If (a(1) + a(2) +...

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