Q. 29 - Calculus

Question

Write out each sum in Exercises 29 in expanded form, and then calculate the value of the sum.

$\sum _{k=4}^9{k}^2$

Step-by-Step Solution

Answer

The expanded notation is $\begin{array}{rcl}& & 4^2+5^2+6^2+7^2+8^2+9^2\end{array}$ and their sum is $271$.

Step 1: Given information

The given summation is $\sum _{k=4}^9{k}^2$.

Step 2: Write the summation in expanded form and evaluate the sum.

Rewrite the given summation in expanded form.

$\begin{array}{rcl}\sum _{k=4}^9{k}^2& =& 4^2+5^2+6^2+7^2+8^2+9^2\\ & =& 16+25+36+49+64+81\\ & =& 271\end{array}$

Step 3: Write the conclusion

The expanded form is $\begin{array}{rcl}& & 4^2+5^2+6^2+7^2+8^2+9^2\end{array}$.

The sum is $271$.