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BITSAT2024MathematicsSequences and SeriesActual

The sum of the infinite series 1+ 5 6 + 12 6^2 + 22 6^3 + 35 6^4 + 51 6^5 + 70 6^6 + . . is equal to:

Options

  1. A425 216
  2. B429 216
  3. C288 125
  4. D280 125

Correct answer

C. 288 125

Step-by-step solution

Let S=1+ 5 6 + 12 6^2 + 22 6^3 + 35 6^4 + .....(i) S 6 = 1 6 + 5 6^2 + 12 6^3 + 22 6^4 + ....(ii) On subtracting (i) from (ii) 5 6 S=1+ 4 6 + 7 6^2 + 10 6^3 + 13 6^4 + 5 36 S= 1 6 + 4 6^2 + 7 6^3 + 10 6^4 + 13 6^5 + on subtraction 25 36 S=1+ 3 6 + 3 6^2 + 3 6^3 + = 8 5 S= 8 5 36 25 = 288 125

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