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3. For all positive integer n, We use indoctior For n=1 $1²=1

3. For all positive integer n, We use indoctior For n=1 $1²=1

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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Use the induction method

 

For all positive integers \( n \), \[ \sum_{k=1}^{n} k^2 = \frac{n(n+1)(2n+1)}{6}. \] We use induction on \( n \). For \( n = 1 \), \[ \sum_{k=1}^{1} k^2 = 1 = \frac{1(2)(3)}{6}. \]
Transcribed Image Text:For all positive integers \( n \), \[ \sum_{k=1}^{n} k^2 = \frac{n(n+1)(2n+1)}{6}. \] We use induction on \( n \). For \( n = 1 \), \[ \sum_{k=1}^{1} k^2 = 1 = \frac{1(2)(3)}{6}. \]
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