If the sum of series 1 1 (1+d) + 1 (1+d)(1+2d) + + 1 (1+9d)(1+10d) is equal to 5, then 50d is equal to

JEE Main 2024 Mathematics question

If the sum of series is equal to 5, then 50d is equal to

Answer: (B)

Each term is 1/((1 + (k − 1)d)(1 + kd)) = (1/d)[1/(1 + (k − 1)d) − 1/(1 + kd)], so the sum telescopes to

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Question ID VK-016546