CBSE  /  Class 11  /  Maths  /  Principle of Mathematical Induction

  • 1. 
    The sum of the series 1³ + 2³ + 3³ + ………..n³ is

  • {(n + 1)/2}²
  • {n/2}²
  • n(n + 1)/2
  • {n(n + 1)/2}²

  • 2. 
    If n is an odd positive integer, then an + bn is divisible by :

  • a² + b²
  • a + b
  • a – b
  • none of these

  • 3. 
    1/(1 ∙ 2) + 1/(2 ∙ 3) + 1/(3 ∙ 4) + ….. + 1/{n(n + 1)}

  • n(n + 1)
  • n/(n + 1)
  • 2n/(n + 1)
  • 3n/(n + 1)

  • 4. 
    The sum of the series 1² + 2² + 3² + ………..n² is

  • n(n + 1)(2n + 1)
  • n(n + 1)(2n + 1)/2
  • n(n + 1)(2n + 1)/3
  • n(n + 1)(2n + 1)/6

  • 5. 
    {1 – (1/2)}{1 – (1/3)}{1 – (1/4)} ……. {1 – 1/(n + 1)} =

  • 1/(n + 1) for all n ∈ N.
  • 1/(n + 1) for all n ∈ R
  • n/(n + 1) for all n ∈ N.
  • n/(n + 1) for all n ∈ R

  • 6. 
    For any natural number n, 7n – 2n is divisible by

  • 3
  • 4
  • 5
  • 7

  • 7. 
    1/(1 ∙ 2 ∙ 3) + 1/(2 ∙ 3 ∙ 4) + …….. + 1/{n(n + 1)(n + 2)} =

  • {n(n + 3)}/{4(n + 1)(n + 2)}
  • (n + 3)/{4(n + 1)(n + 2)}
  • n/{4(n + 1)(n + 2)}
  • None of these

  • 8. 
    The nth terms of the series 3 + 7 + 13 + 21 +………. is

  • 4n – 1
  • n² + n + 1
  • none of these
  • n + 2

  • 9. 
    n(n + 1)(n + 5) is a multiple of ____ for all n ∈ N

  • 2
  • 3
  • 5
  • 7

  • 10. 
    Find the number of shots arranged in a complete pyramid the base of which is an equilateral triangle, each side containing n shots.

  • n(n+1)(n+2)/3
  • n(n+1)(n+2)/6
  • n(n+2)/6
  • (n+1)(n+2)/6
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