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Manipal MET2015MathematicsSequences and Series

The sum to 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 be the sum of the given series. i.e. S=1+ 2 3 + 6 3^2 + 10 3^3 + (S-1)= 2 3 + 6 3^2 + 10 3^3 + ...(i) (S-1) 1 3 = 2 3^2 + 6 3^3 + 10 3^4 + ...(ii) On subtracting Eq. (ii) from Eq. (i), we get 2 3 (S-1)= 2 3 + 4 3^2 + 4 3^3 + 4 3^4 + 2 3 (S-1)= 2 3 + 4 3^2 1- 1 3 2 3 (S-1)= 2 3 + 2 3 S-1 S=3

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