JEE Main 2022 Mathematics question
Let for n = 1, 2, …, 50, be the sum of the infinite geometric progression whose first term is and whose common ratio is 1/(n + . Then the value of + 2/(n + 1) − n − 1) is equal to .
Answer: 41651
Solution
− 1/(n + ) − 2/(n + 2). So + 2/(n + + 2(1/(n + 1) − 1/(n + 2)). Summing for n = 1
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