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

Problem

(∑_k=1^5)(k2)

Solution

1. Identify the upper limit of the summation, which is n=5

2. Recall the power sum formula for the sum of the first n squares.

(∑_k=1^n)(k2)=(n*(n+1)*(2*n+1))/6

3. Substitute the value n=5 into the formula.

(∑_k=1^5)(k2)=(5*(5+1)*(2*(5)+1))/6

4. Simplify the expression inside the parentheses.

(∑_k=1^5)(k2)=(5*(6)*(11))/6

5. Calculate the final value by canceling the common factor of 6

(∑_k=1^5)(k2)=5⋅11

(∑_k=1^5)(k2)=55

Final Answer

(∑_k=1^5)(k2)=55

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