Evaluate the Summation sum from k=1 to 12 of k^2

Problem

(∑_k=1^12)(k2)

Solution

1. Identify the formula for the sum of the first n squares. The sum of squares is given by the formula:

(∑_k=1^n)(k2)=(n*(n+1)*(2*n+1))/6

2. Substitute the upper limit of the summation, n=12 into the formula:

(∑_k=1^12)(k2)=(12*(12+1)*(2*(12)+1))/6

3. Simplify the terms inside the parentheses:

(∑_k=1^12)(k2)=(12*(13)*(25))/6

4. Divide 12 by 6 to simplify the fraction:

(∑_k=1^12)(k2)=2*(13)*(25)

5. Multiply the remaining factors to find the final value:

(∑_k=1^12)(k2)=26*(25)=650

Final Answer

(∑_k=1^12)(k2)=650

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