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Home » Question: Compute $ \sum_n=1^50 \frac1n(n+2) $. - High Altitude Science

Question: Compute $ \sum_n=1^50 \frac1n(n+2) $. - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 S_5 = 3 + 6 + 12 + 24 + 48 = 93

📌 S_n = a \frac{r^n - 1}{r - 1}

📌 المخروط له نصف قطر قاعدة 3 وحدات وارتفاع 4 وحدات. ما هو الارتفاع المائل للمخروط؟

📌 يتم إيجاد الارتفاع المائل \( l \) باستخدام نظرية فيثاغورس:

📌 l = \sqrt{r^2 + h^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5

📌 مجموع أول \( n \) عدد طبيعي هو 210. ما هي \( n \)؟

📌 يُعطى مجموع أول \( n \) عدد طبيعي بالصيغة:

📌 \frac{n(n + 1)}{2} = 210

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