Question

Evaluating a Sum Find the sum.

$\sum _{i=1}^{3}i{2}^i$

Short answer

The sum is 34.

Step-by-step solution

Step 1.  Given

The given sequence is$\sum _{i=1}^{3}i{2}^i.$

Step 2.  To determine

We have to find thesum of the given sequence.

Step 3.  Calculation

We’ll plug the values of i and get rid of the summation sign to simplify:

$\begin{array}{l}\sum _{i=1}^{3}i{2}^i\\ =\left(1\times 2^1\right)+\left(2\times 2^2\right)+\left(3\times 2^3\right)\\ =2+8+24\\ =34\end{array}$

Hence, the sum is 34.