Question

Sigma Notation Write the sum without using sigma notation.

$\sum _{k=6}^{9}k\left(k+3\right)$

Short answer

The sum is$6\left(9\right)+7\left(10\right)+8\left(11\right)+9\left(12\right).$

Step-by-step solution

Step 1.  Given

The given sequence is$\sum _{k=6}^{9}k\left(k+3\right)$.

Step 2.  To determine

We have to write the sum without using sigma notation.

Step 3.  Calculation

We’ll plug the values for k, to get rid of the sigma notation.

$\begin{array}{l}\sum _{k=6}^{9}k\left(k+3\right)\\ =\left[6\left(6+3\right)\right]+\left[7\left(7+3\right)\right]+\left[8\left(8+3\right)\right]+\left[9\left(9+3\right)\right]\\ =\left[6\left(9\right)\right]+\left[7\left(10\right)\right]+\left[8\left(11\right)\right]+\left[9\left(12\right)\right]\\ =6\left(9\right)+7\left(10\right)+8\left(11\right)+9\left(12\right)\end{array}$

Hence the sum is$6\left(9\right)+7\left(10\right)+8\left(11\right)+9\left(12\right)$.