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The value of the expression ( 1 + (1)...

The value of the expression
`( 1 + (1)/(omega)) ( 1 + (1)/(omega^(2))) + (2 + (1)/(omega)) (2 + (1)/(omega^(2))) + (3 + (1)/(omega)) (3 + (1)/(omega^(2))) + …… + ((n + (1))/(omega)) (n + (1)/(omega^(2)))`
Where `omega` is an imaginary cube root of unity, is

A

`(n(n^(2) + 2))/(3)`

B

`(n(n^(2) - 2))/(3)`

C

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

D

none of these

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Verified by Experts

The correct Answer is:
A
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DIPTI PUBLICATION ( AP EAMET)-SEQUENCES AND SERIES -EXERCISE
  1. Sum of the series S = 1 + (1)/(2)(1 + 2) + (1)/(3) ( 1 + 2 + 3 ) + (1)...

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  2. If 1^(2)+2^(2)+3^(2)+…..+2003^(2)=(2003)(4007)(334)and(1)(2003)+(2)(20...

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  3. The value of the expression ( 1 + (1)/(omega)) ( 1 + (1)/(omega^(2)...

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  4. If 2nd term of a G.p. is 24 and 5th terms is 81 then the first term is

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  5. If 6th term of a G.P is -1/32 and 9th term is 1/1256, then 11th term =

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  6. Which term of 0.004 + 0.02 + 0.1 + ….. Is 12.5 ?

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  7. Which term of the series 1,2,4,8,……… is 256?

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  8. Sum of 20 terms of 3 + 6 + 12 + …. Is

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  9. If nth term of series is 2^(n) + n, then sum of n terms =

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  10. If 5th term of a G.P is 32 and common ratio 2, then the sum of 14 term...

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  11. How many terms of the series 1 + 3 + 9 + …. Sum to 364 ?

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  12. If (1 - y) (1 + 2x + 4x^(2) + 8x^(3) + 16x^(4) + 32x^(5)) = 1 -y^(6), ...

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  13. In a geometric progression consisting of positive terms each term equa...

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  14. 1 + (0.04) + (0.04)^(2) + …. infty =

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  15. If |x| lt 1, y = x - x^(2) + x^(3) - x^(4) + ….. , the value of x in t...

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  16. If x = 1 + a + a^(2) + …. infty " , " y = 1 + b + b^(2) + …...

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  17. If x = sum(n = 0)^(infty) a^(n) , y = sum(n = 0)^(infty) b^(n) , z = s...

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  18. If exp{ (sin^(2) x + sin^(4) x + sin^(6) x + …. "Upto" infty) log(e) 2...

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  19. If exp { (tan^(2) x -tan^(4) x + tan^(8) x - tan^(6) x …. ) log(e) 16 ...

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  20. For 0 lt x lt pi the values of x which satisfy the relation 9^(1 + ...

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