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Home » How The Marquise Diamond Engagement Ring tops Every Budget—Luxury Redefined! - IQnection

How The Marquise Diamond Engagement Ring tops Every Budget—Luxury Redefined! - IQnection

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Question: What is the remainder when $ 1001 + 1003 + 1005 + \cdots + 1099 $ is divided by $ 16 $?

📌 Solution: The sequence is an arithmetic series of odd numbers from 1001 to 1099, inclusive.

📌 First, find the number of terms. This is an arithmetic sequence with:

📌 First term $ a = 1001 $

📌 Common difference $ d = 2 $

📌 Last term $ l = 1099 $

📌 n = \frac{1099 - 1001}{2} + 1 = \frac{98}{2} + 1 = 49 + 1 = 50

📌 Sum of arithmetic series:

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