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Sum of the series S=t^(2) - 2^(2) + 3^(2...

Sum of the series `S=t^(2) - 2^(2) + 3^(2) - 4^(2) + …... - 2002^(2) + 2003^(2)` is

A

`2007006`

B

`1005004`

C

`2000506`

D

`207006`

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The correct Answer is:
A
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AAKASH SERIES-MATHEMATICAL INDUCTION-PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)
  1. If 2^(3) + 4^(3) + 6^(3) + … + (2n)^(3) = kn^(2) ( n+1)^(2) then k=

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  2. 4^(3) + 5^(3) + 6^(3) + … + 10^(3)

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  3. Sum of the series S=t^(2) - 2^(2) + 3^(2) - 4^(2) + …... - 2002^(2) + ...

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  4. (sumn^(3) ) ( sumn) = (sumn^2) ^2 if

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  5. n^( th) term of the series 4+14+ 30 + 52+ …..

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  6. If 1+ 5+ 12+ 22 + 35+ ….. + to n terms = ( n^(2) (n+1) )/(2) then n^...

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  7. 1+ 3+ 7 + 15…n terms =

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  8. 1^(2) + 3^(2) + 5^(2) + …. upto n terms =

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  9. 2+ 3.2 + 4.2^(2) + …... upto n terms =

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  10. (1^(2) )/( 1) + (1^(2) + 2^(2) )/(1+2) + (1^(2) + 2^(2) + 3^(2) )/( 1...

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  11. Sum of first 'n' terms of the series = (3)/(2) + (5)/(4) + (9)/(8) + (...

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  12. 0.2 + 0.22 + 0.222+ …. upto n terms is equal to

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  13. 2+7+14+…..+ (n^(2) + 2n-1)=

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  14. 1.6 + 2.9+ 3.12+ ….. + n ( 3n+3)=

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  15. 2.4 + 4.7 + 6.10+ …. upto (n-1) terms=

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  16. sum(n=0)^( oo) (-1)^(n) x^( n+1)=

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  17. sum(k=1)^(2n+1) (-1)^(k-1) k^2 =

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  18. cos theta + cos 2 theta + cos 3 theta + …. + cos { (n-1) theta}+ cos n...

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  19. If P (n) = 1+2+3+ …. + n is a perfect square N^(2) and N is less than...

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  20. 1 + (x)/( a1) + ( x( x+a1) )/( a1 a2 ) + .... + ( x ( x+a1) (x+ a2)......

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