Find the sum. 5 Σk² k = 1
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![Find the sum.
\[
\sum_{k=1}^{5} k^2
\]
In this mathematical expression, we are asked to find the sum of the squares of the first five positive integers. The sigma notation (∑) indicates summation, and the expression below it is called the index of summation, which starts at \( k = 1 \) and ends at \( k = 5 \). The expression \( k^2 \) signifies that each integer \( k \) should be squared before summing.
To compute this, you calculate:
- \( 1^2 = 1 \)
- \( 2^2 = 4 \)
- \( 3^2 = 9 \)
- \( 4^2 = 16 \)
- \( 5^2 = 25 \)
Finally, add these results:
\[ 1 + 4 + 9 + 16 + 25 = 55 \]
So the sum is 55.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3f7f0de7-1870-4369-970d-744d96e626bb%2F60aebbab-f4ce-4a83-b9ba-c525dc28b6d6%2Fzdwe2vo_processed.png&w=3840&q=75)
Transcribed Image Text:Find the sum.
\[
\sum_{k=1}^{5} k^2
\]
In this mathematical expression, we are asked to find the sum of the squares of the first five positive integers. The sigma notation (∑) indicates summation, and the expression below it is called the index of summation, which starts at \( k = 1 \) and ends at \( k = 5 \). The expression \( k^2 \) signifies that each integer \( k \) should be squared before summing.
To compute this, you calculate:
- \( 1^2 = 1 \)
- \( 2^2 = 4 \)
- \( 3^2 = 9 \)
- \( 4^2 = 16 \)
- \( 5^2 = 25 \)
Finally, add these results:
\[ 1 + 4 + 9 + 16 + 25 = 55 \]
So the sum is 55.
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