Evaluate the Summation sum from k=1 to 25 of k^2

Problem

(∑_k=1^25)(k^2)

Solution

1. Identify the formula for the sum of the first n squares, which is given by the expression for (∑_k=1^n)(k^2)

(∑_k=1^n)(k^2)=(n*(n+1)*(2*n+1))/6

2. Substitute the value n=25 into the formula to evaluate the specific summation.

(∑_k=1^25)(k^2)=(25*(25+1)*(2*(25)+1))/6

3. Simplify the terms inside the parentheses.

(∑_k=1^25)(k^2)=(25*(26)*(51))/6

4. Calculate the product in the numerator.

25×26×51=33150

5. Divide the result by 6 to find the final value.

33150/6=5525

Final Answer

(∑_k=1^25)(k^2)=5525

Want more problems? Check here!