Chapter 11.4, Problem 3WE

To determine

To calculate:

Given series in expanded form.

Answer to Problem 3WE

Series in expanded form is $2.097\times {10}^6$ .

Explanation of Solution

Give information:

Expression:

  ${\displaystyle \sum _{n=1}^6{2}^n}$

It is given that,

  ${\displaystyle \sum _{n=1}^6{2}^n}$

So, for expanded form,

Put the values $n$ in equation,

  $\begin{array}{l}={\displaystyle \sum _{n=1}^6{2}^n}\\ =\left(2^1\right)+\left(2^2\right)+\left(2^3\right)+\left(2^4\right)+\left(2^5\right)+\left(2^6\right)\\ =\left(2\right)\left(4\right)+\left(8\right)+\left(16\right)+\left(32\right)+\left(64\right)\\ =2.097\times {10}^6\end{array}$

Therefore, series in expanded form is $2.097\times {10}^6$ .