Chapter 12.5, Problem 28E

To determine

To express the given series using sigma notation.

Answer to Problem 28E

  ${\displaystyle \sum _{n=0}^4\left(4^n\right)}$

Explanation of Solution

Given information:

Given series is,

1 + 4 + 16 + . . . + 256

Here we can write $1=4^0,4=4^1,16=4^2$

Given series can be written in form $4^n$

Where $n$ can take values from 0 to 4.

Hence series using sigma notation is,

  ${\displaystyle \sum _{n=0}^4\left(4^n\right)}$