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If n EN, then 1-3+2-4+3-5+4-6+...+ n(n+2) = n(n+1)(2n+7) 6

If n EN, then 1-3+2-4+3-5+4-6+...+ n(n+2) = n(n+1)(2n+7) 6

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**7.** If \( n \in \mathbb{N} \), then \( 1 \cdot 3 + 2 \cdot 4 + 3 \cdot 5 + 4 \cdot 6 + \cdots + n(n+2) = \frac{n(n+1)(2n+7)}{6} \). This equation illustrates a series sum involving natural numbers and shows its equivalence to a specific formula. The summation on the left involves terms where each natural number \( n \) is multiplied by \( n+2 \), and the right side provides a closed-form expression for calculating this sum.
Transcribed Image Text:**7.** If \( n \in \mathbb{N} \), then \( 1 \cdot 3 + 2 \cdot 4 + 3 \cdot 5 + 4 \cdot 6 + \cdots + n(n+2) = \frac{n(n+1)(2n+7)}{6} \). This equation illustrates a series sum involving natural numbers and shows its equivalence to a specific formula. The summation on the left involves terms where each natural number \( n \) is multiplied by \( n+2 \), and the right side provides a closed-form expression for calculating this sum.
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