Evaluate the Summation sum from k=1 to 5 of k^2

Problem

(∑_k=1^5)(k2)

Solution

1. Identify the terms of the summation by substituting each integer value of k from 1 to 5 into the expression k2

2. Calculate the square of each value:

1=1

2=4

3=9

4=16

5=25

3. Sum the resulting values together:

1+4+9+16+25

4. Simplify the addition to find the total:

1+4=5

5+9=14

14+16=30

30+25=55

Final Answer

(∑_k=1^5)(k2)=55

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