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Let S = 2 + 6 7 + 12 7 2 + 20 7 3 + 30 7 4 + … . . then 4 S is equal to

Options

  1. A7 2 2
  2. B7 3 3
  3. C7 3
  4. D7 3 4

Correct answer

B. 7 3 3

Step-by-step solution

S = 2 + 6 7 + 12 7 2 + 20 7 3 + ⋯       . . . i S 7 = 0 + 2 7 + 6 7 2 + 12 7 3 + 20 7 4 + ⋯       . . . i i On subtracting the equation i i from equation i , we get 6 S 7 = 2 + 4 7 + 6 7 2 + 8 7 3 + ⋯       . . . i i i 6 S 49 = 0 + 2 7 + 4 7 2 + 6 7 3 + ⋯       . . . i v On subtracting the equation i v from equation i i i , we get 6 7 - 6 49 S = 2 + 2 7 + 2 7 2 + 2 7 3 + ⋯ 36 49 S = 2 1 + 1 7 + 1 7 2 + ⋯ ∞ ⇒

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