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:

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Correct answer: C. 288 125

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

BITSAT Mathematics Question (2024) — Solution

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