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The sum of the series 5 1 2 ⋅ 4 2 + 11 4 2 ⋅ 7 2 + 17 7 2 ⋅ 10 2 + . … … . is

Options

  1. A1 2
  2. B1 3
  3. C2
  4. D3

Correct answer

B. 1 3

Step-by-step solution

S = 5 1 2 ⋅ 4 2 + 11 4 2 ⋅ 7 2 + 17 7 2 ⋅ 10 2 + . … 3 S = 3.5 1 2 ⋅ 4 2 + 3 ⋅ 11 4 2 ⋅ 7 2 + 3 ⋅ 17 7 2 ⋅ 10 2 + . … . 3 S = 4 - 1 4 + 1 1 2 ⋅ 4 2 + 7 - 4 7 + 4 4 2 · 7 2 + 10 - 7 10 + 7 7 2 ⋅ 10 2 + . … . 3 S = 4 2 - 1 2 1 2 ⋅ 4 2 + 7 2 - 4 2 4 2 ⋅ 7 2 + 10 2 - 7 2 7 2 ⋅ 10 2 + . … . = 1 1 2 - 1 4 2 + 1 4 2 - 1 7 2 + 1 7 2 - 1 10 2 + . … . ⇒ 3 S = 1 S = 1 3

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