Question

Sigma Notation Write the sum without using sigma notation.

$\sum _{k=3}^{100}{x}^k$

Short answer

The sum is$x^3+x^4+x^5+\mathrm{.....}+x^{100}$.

Step-by-step solution

Step 1.  Given

The given sequence is $\sum _{k=3}^{100}{x}^k$.

Step 2.  To determine

We have to write the sum without using sigma notation.

Step 3.  Calculation

We’ll plug the values for k, to get rid of the sigma notation.

$\begin{array}{l}\sum _{k=3}^{100}{x}^k\\ =x^3+x^4+x^5+\mathrm{.....}+x^{100}\end{array}$

Hence the sum is $x^3+x^4+x^5+.....+x^{100}$.