Chapter 12, Problem 4RCC

To determine

Calculate the sum of the ${\displaystyle \sum _{k=1}^n{a}_k}$ without using sigma notation.

Answer to Problem 4RCC

The final summation of ${\displaystyle \sum _{k=1}^n{a}_k}$ is $a_1+a_2+a_3+a_4+a_5+a_6+\mathrm{..........}+a_{n-2}+a_{n-1}+a_n$ .

Explanation of Solution

Given information:

It is given in the question that, ${\displaystyle \sum _{k=1}^n{a}_k}$

By evaluating the given summation ${\displaystyle \sum _{k=1}^n{a}_k}$ ,

by using the method of expanding

  $a_1+a_2+a_3+a_4+a_5+a_6+\mathrm{..........}+a_{n-2}+a_{n-1}+a_n$

The final summation of ${\displaystyle \sum _{k=1}^n{a}_k}$ is $a_1+a_2+a_3+a_4+a_5+a_6+\mathrm{..........}+a_{n-2}+a_{n-1}+a_n$ .