If 5_ 1 , 5_ 2 , 5_ 3 5_ n are the sum of infinite geometric series whose first terms are…
Mathematics · JEE Main · NTA Exams — Progression and Series
If \(5_{1}, 5_{2}, 5_{3} \ldots 5_{n}\) are the sum of infinite geometric series whose first terms are 1, 2, 3,......n and common ratio are \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \ldots \ldots \frac{1}{n+1}\) respectively then, find the value of \(5_{1}+5_{2}+5_{3}+\ldots+5_{n}\).
- \(\frac{\pi}{2}(n+1)\)
- \(\frac{n}{3}(n+1)(n+2)\)
- \(\frac{n}{2}(n+1)(2 n+1)\)
- \(\frac{\pi}{2}(n+3)\)
Answer
(B) n 3 (n+1)(n+2)
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