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
If n is an odd positive integer, then an + bn is divisible by :
  • a² + b²
  • a + b
  • a – b
  • none of these
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)
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
{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
For any natural number n, 7n – 2n is divisible by
  • 3
  • 4
  • 5
  • 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
The nth terms of the series 3 + 7 + 13 + 21 +………. is
  • 4n – 1
  • n² + n + 1
  • none of these
  • n + 2
n(n + 1)(n + 5) is a multiple of ____ for all n ∈ N
  • 2
  • 3
  • 5
  • 7
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
(n² + n) is ____ for all n ∈ N.
  • Even
  • odd
  • Either even or odd
  • None of these
For all n ∈ N, 3×52n+1 + 23n+1 is divisible by
  • 19
  • 17
  • 23
  • 25
(1 + x)n ≥ ____ for all n ∈ N,where x > -1
  • 1 + nx
  • 1 – nx
  • 1 + nx/2
  • 1 – nx/2
102n-1 + 1 is divisible by ____ for all N ∈ N
  • 9
  • 10
  • 11
  • 13
{1/(3 ∙ 5)} + {1/(5 ∙ 7)} + {1/(7 ∙ 9)} + ……. + 1/{(2n + 1)(2n + 3)} =
  • n/(2n + 3)
  • n/{2(2n + 3)}
  • n/{3(2n + 3)}
  • n/{4(2n + 3)}
0 h : 0 m : 1 s

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