Chapter 12.1, Problem 59E

To determine

Find the sum of the given function ${\displaystyle \sum _{K=3}^{100}{x}^k}$ without using sigma notation.

Answer to Problem 59E

The sum of the given term is $x^3+x^4+x^5+\mathrm{..........}+x^{99}+x^{100}$ .

Explanation of Solution

Given information:

It is given in the question that,

The function is ${\displaystyle \sum _{K=3}^{100}{x}^k}$ .

By putting the value of $K=3,4,5,6,7,8,9,10,\mathrm{........100}$ in ${\displaystyle \sum _{K=3}^{100}{x}^k}$ (summation) the following term is arrived,

  $\Rightarrow x^3+x^4+x^5+\mathrm{..........}+x^{99}+x^{100}$ .