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Home » Initial number of T-cells, \( N_0 = 1,000 \) - inBeat

Initial number of T-cells, \( N_0 = 1,000 \) - inBeat

📅 May 3, 2026 👤 scraface

May 03, 2026

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Question: What is the remainder when $ 1001 + 1003 + 1005 + \cdots + 1...
Solution: The sequence is an arithmetic series of odd numbers from 100...
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:
S = \frac{n}{2}(a + l) = \frac{50}{2}(1001 + 1099) = 25 \cdot 2100 = 5...
Now compute $ 52500 \mod 16 $.

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