The given series starts with $17$, and the next term is $34$, then $57$, and so on until $5126$. This suggests that the series is arithmetic, where the difference between consecutive terms is constant.

Steps to represent this in sigma notation:

1. Identify the first term ($a$): The first term $a = 17$.

2. Find the common difference ($d$): The second term is $34$, and the first term is $17$, so the common difference is: $d = 34 - 17 = 17.$

3. Find the number of terms ($n$): The general form for the $n$-th term of an arithmetic sequence is: $a_n = a + (n-1) \cdot d.$ The last term is $5126$, so: $5126 = 17 + (n-1) \cdot 17.$ Simplifying this equation: $5126 - 17 = (n-1) \cdot 17,$ $5109 = (n-1) \cdot 17,$ $n-1 = \frac{5109}{17} = 300,$ $n = 301.$ So, there are $301$ terms.

4. Write the sigma notation: The arithmetic series can be expressed in sigma notation as: $\sum_{k=1}^{301} \left( 17k \right).$

Thus, the sigma notation for the series is: $\sum_{k=1}^{301} \left( 17k \right).$

Would you like any further explanation or details on this?

Related Questions:

1. How do you calculate the sum of an arithmetic series using sigma notation?
2. What is the formula for the sum of the first $n$ terms in an arithmetic series?
3. Can this series be expressed in a different way using sequences?
4. How do you derive the general formula for the $n$-th term in an arithmetic series?
5. What are some common applications of sigma notation in calculus?

Tip: The sum of an arithmetic series can be calculated using the formula $S_n = \frac{n}{2} \cdot (a + l)$, where $a$ is the first term, $l$ is the last term, and $n$ is the number of terms.