JEE Main 2024 Mathematics question
If up to ∞ = , where a and b are integers with gcd(a, b) = 1, then 11a + 18b is equal to .
Answer: 76
Solution
The terms are t/2, t²/6, t³/12, t⁴/20, … with t = 1 − √(2/3), so the series is 1 + Σ tⁿ/(n(n + 1)) = 2 + (1/t − 1) ln(1 − t). Here 1/t − 1 = √6 + 2 and ln(1 − t) = −½ ln(3/2), giving 2 +
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