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The sum of first n terms of the series ...

The sum of first n terms of the series
`1^(2) + 2.2^(2) +3^(2) + 2. 4^(2) + 5^(2) + 2. 6^(2) + "........."` is `( n ( n + 1)^(2))/( 2)` when n is even. When, n is odd, the sum is `:`

A

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

B

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

C

`( n ( n +1)^(2))/( 4)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
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MODERN PUBLICATION-SEQUENCES AND SERIES -MCQ ( Level-II)
  1. The first term of a G. P. is 1. The sum of the third and fifth terms i...

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

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

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

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

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

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

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  9. If a(r ) gt 0, r in N and a(1), a(2) , a(3) ,"……..",a(2n) are in A.P....

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  10. Let x,y,z be three positive prime numbers. The progression in which sq...

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  11. If x = sum(n=0)^(oo) a^(n) .,y=sum(n=0)^(oo) b^(n) , z = sum(n=0)^(oo)...

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  12. underset("n-digits")((666"……"6))^(2) +underset("n-digits") (( 888"…" 8...

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  13. If sum(r=1)^(n) t(r ) = sum(k=1)^(n) sum(j=1)^(k) sum(i=1)^(j) 2, then...

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  14. The odd numbers are divides as follows : {:(,,1,3,,),(,5,7,9,11,),(1...

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  15. If x(1), x(2), x(3) as well as y(1) , y (2) , y (3) are in G.P. with t...

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  16. If a(1) , a(2), "……………" a(n) are in H.P., then the expression a(1) a(2...

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  17. In a geometric progression consisting of positive terms, each term equ...

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  18. The first two terms of a geometric progression add upto 12. The sum of...

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  19. The sum to infinity of the series : 1+ ( 2)/( 3) + ( 6)/( 3^(2)) +(...

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  20. If the sum of first n terms of an A.P. is cn^(2) , then the sum of squ...

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