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For all n in N, x in R, tan^(-1) [ ( x)/...

For all `n in N, x in R, tan^(-1) [ ( x)/( 1.2+ x^2) ] + tan^(-1) [ (x)/( 2.3+ x^2) ] + …. + tan^(-1) [ ( x)/( n(n+1) +x^2) ] =`

A

`tan^(-1) [ (x)/( n) ] - tan^(-1) [ (x)/( n+1) ]`

B

`tan^(-1) [x] - tan^(-1) [ (x)/( n+1) ]`

C

`tan^(-1) [n+1] - tan^(-1) [x]`

D

`tan^(-1) [x]`

Text Solution

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The correct Answer is:
B
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AAKASH SERIES-MATHEMATICAL INDUCTION-PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)
  1. For all n in N, x in R, tan^(-1) [ ( x)/( 1.2+ x^2) ] + tan^(-1) [ (x)...

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  2. Let P(n) denote the statement that n^(2) +n is odd. It is seen that P(...

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  3. The statement P(n) (1xx1!) + (2 xx2!) + (3 xx 3!) + … …. + (nxx n!) = ...

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  4. If P(n) be the statement n (n+1)+1 is an integer, then which of the fo...

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  5. n gt 1, n even rArr digit in the units place of 2^(2n)+1

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  6. log ( x )^(n) = n .log x is true for n.

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  7. If 2^(3) + 4^(3) + 6^(3) + … + (2n)^(3) = kn^(2) ( n+1)^(2) then k=

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  8. 4^(3) + 5^(3) + 6^(3) + … + 10^(3)

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

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

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

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

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  13. 1+ 3+ 7 + 15…n terms =

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  14. 1^(2) + 3^(2) + 5^(2) + …. upto n terms =

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  15. 2+ 3.2 + 4.2^(2) + …... upto n terms =

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  16. (1^(2) )/( 1) + (1^(2) + 2^(2) )/(1+2) + (1^(2) + 2^(2) + 3^(2) )/( 1...

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

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  18. 0.2 + 0.22 + 0.222+ …. upto n terms is equal to

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  19. 2+7+14+…..+ (n^(2) + 2n-1)=

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  20. 1.6 + 2.9+ 3.12+ ….. + n ( 3n+3)=

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  21. 2.4 + 4.7 + 6.10+ …. upto (n-1) terms=

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