What is the sum of the given summation notation below?

To find the sum of the given summation notation, we need to evaluate the summation expression. The summation notation provided is: \[ \sum_{n=1}^{10} n^2 \] This notation represents the sum of the squares of the numbers from 1 to 10. To find the sum, we need to calculate the sum of the squares of the numbers from 1 to 10. Let's calculate the sum of the squares of the numbers from 1 to 10: \[ 1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 + 8^2 + 9^2 + 10^2 \] Now, we can calculate the sum of these squares to find the result. Calculate the value by following steps: - step0: Calculate: \(1^{2}+2^{2}+3^{2}+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}\) - step1: Evaluate the power: \(1+2^{2}+3^{2}+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}\) - step2: Evaluate the power: \(1+4+3^{2}+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}\) - step3: Evaluate the power: \(1+4+9+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}\) - step4: Evaluate the power: \(1+4+9+16+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}\) - step5: Evaluate the power: \(1+4+9+16+25+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}\) - step6: Evaluate the power: \(1+4+9+16+25+36+7^{2}+8^{2}+9^{2}+10^{2}\) - step7: Evaluate the power: \(1+4+9+16+25+36+49+8^{2}+9^{2}+10^{2}\) - step8: Evaluate the power: \(1+4+9+16+25+36+49+64+9^{2}+10^{2}\) - step9: Evaluate the power: \(1+4+9+16+25+36+49+64+81+10^{2}\) - step10: Evaluate the power: \(1+4+9+16+25+36+49+64+81+100\) - step11: Add the numbers: \(385\) The sum of the given summation notation \(\sum_{n=1}^{10} n^2\) is 385.