Chapter 12.5, Problem 31E

To determine

To express the given series using sigma notation.

Answer to Problem 31E

  ${\displaystyle \sum _{n=1}^4\left(2\cdot 5^n\right)}$

Explanation of Solution

Given information:

Given series is,

10 + 50 + 250 + 1250

Here we can write $10=\left(2\cdot 5\right),50=\left(2\cdot 5^2\right),250=\left(2\cdot 5^3\right)$

Given series can be written in form $\left(2\cdot 5^n\right)$

Where $n$ can take values from 1 to 4.

Hence series using sigma notation is,

  ${\displaystyle \sum _{n=1}^4\left(2\cdot 5^n\right)}$