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The sum 1 + 2 · 3 + 3 · 3 2 + … … . . + 10 · 3 9 is equal to

Options

  1. A2 · 3 12 + 10 4
  2. B19 · 3 10 + 1 4
  3. C5 · 3 10 - 2
  4. D9 · 3 10 + 1 2

Correct answer

B. 19 · 3 10 + 1 4

Step-by-step solution

Let S = 1 · 3 0 + 2 · 3 1 + 3 · 3 2 + … . . + 10 . 3 9 ....(i) 3 S = 1 . 3 1 + 2 . 3 2 … … … … … … . + 9 × 3 9 + 10 × 3 10 .....(ii) Now subtracting equation (ii) from (i) we get, - 2   S = 1 · 3 0 + 3 1 + 3 2 … . . 3 9 - 10 . 3 10 S = 5 × 3 10 - 3 10 - 1 4 S = 20 . 3 10 - 3 10 + 1 4 = 19 . 3 10 + 1 4

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