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The sum to the infinity of the series 1+ 2 3 + 6 3^2 + 10 3^3 + 14 3^4 + is

Options

  1. A2
  2. B3
  3. C4
  4. D6

Correct answer

B. 3

Step-by-step solution

Let S=1+ 2 3 + 6 3^2 + 10 3^3 + 14 3^4 + . 1 3 S= 1 3 + 2 3^2 + 6 3^3 + 10 3^4 + Dividing (1) & (2) aligned & S (1- 1 3 )=1+ 1 3 + 4 3^2 + 4 3^3 + 4 3^4 + . & 2 3 S= 4 3 + 4 3^2 (1+ 1 3 + 1 3^2 + . . ) 2 3 S= 4 3 + 4 3^2 ( 1 1- 1 3 )= 4 3 + 4 3^2 3 2 = 4 3 + 2 3 = 6 2 2 3 S= 6 3 S=3 aligned

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