12 + 1 + 22 + 2 + 32 + 3 + ... + n2 + n is equal to fr

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 Multiple Choice QuestionsMultiple Choice Questions

111.

If the arithmetic mean of a and b is an + bnan - 1 + bn - 1, then the value of n is

  • - 1

  • 0

  • 1

  • None of the above


112.

12! + 14! + 16! + ...1 + 13! + 15! + ... equals

  • e + 1

  • e - 1e + 1

  • e - 1

  • None of these


113.

The sum of the series

a - ba + 12a - ba2 + 13a - ba3 + ...  is

  • logeab

  • logea - ba

  • logeba

  • None of these


114.

The harmonic mean of the roots of the equation

5 + 2x2 - 4 + 5x + 8 + 25 = 0 is

  • 2

  • 4

  • 6

  • 8


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115.

The sum of n terms of the following series 1 + (1 + x) + (1 + x + x2) +... will be

  • 1 - xn1 - x

  • x1 - xn1 - x

  • n1 - x - x1 - xn1 - x2

  • None of the above


116.

If A1, A2; G1, G2 and H1, H2 be two AM's, GM's and HM's between two quantities, then the value of G1G2H1H2 is

  • A1 + A2H1 + H2

  • A1 - A2H1 + H2

  • A1 + A2H1 - H2

  • A1 - A2H1 - H2


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117.

12 + 1 + 22 + 2 + 32 + 3 + ... + n2 + n is equal to

  • nn + 12

  • nn + 122

  • nn + 1n + 23

  • nn + 1n + 2n + 34


C.

nn + 1n + 23

Given series is,

12 + 1 + 22 + 2 + 32 + 3 + ... + n2 + n

 Sum = n2 + n = n2 + n             = nn + 12n + 16 + nn + 12            = nn + 12n + 1 + 36            = 2nn + 1n + 26

          = nn + 1n + 23


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118.

21/4 . 41/8 . 81/16 . 161/32 ... is equal to

  • 1

  • 2

  • 32

  • 52


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119.

The sum of the series

- 1rCrn12r + 3r22r + 7r23r + 15r24r + ... m terms is

  • 2mn - 12mn2n - 1

  • 2mn - 12n - 1

  • 2mn + 12n + 1

  • None of these


120.

If n = (1999)!, Then x = 11999lognx is equal to

  • 1

  • 0

  • 19991999

  • - 1


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