S, =E = 12 + 2² + 3² + . . + n² %3D
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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![**Calculate**
\[ S_n = \sum_{i=1}^{n} i^2 = 1^2 + 2^2 + 3^2 + \cdots + n^2 \]
This equation involves calculating the sum of squares of the first \( n \) natural numbers. It is represented as \( S_n \), where \( n \) is the number up to which you want to calculate the sum. The expression \( \sum_{i=1}^{n} i^2 \) indicates that you add up the squares of all integers from 1 to \( n \).
For example, if \( n = 3 \), then:
\[ S_3 = 1^2 + 2^2 + 3^2 = 1 + 4 + 9 = 14 \]
This is a common problem in algebra and number theory, which helps in understanding series and sequences.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe6156c38-2816-48c7-aed8-10dafecc3b80%2Faee1e432-1f13-4744-89c8-0af9719a3ff1%2Fj77w5vr_processed.png&w=3840&q=75)
Transcribed Image Text:**Calculate**
\[ S_n = \sum_{i=1}^{n} i^2 = 1^2 + 2^2 + 3^2 + \cdots + n^2 \]
This equation involves calculating the sum of squares of the first \( n \) natural numbers. It is represented as \( S_n \), where \( n \) is the number up to which you want to calculate the sum. The expression \( \sum_{i=1}^{n} i^2 \) indicates that you add up the squares of all integers from 1 to \( n \).
For example, if \( n = 3 \), then:
\[ S_3 = 1^2 + 2^2 + 3^2 = 1 + 4 + 9 = 14 \]
This is a common problem in algebra and number theory, which helps in understanding series and sequences.
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