In Exercises 10–11, express each sum using summation notation. Use i for the index of summation. 1/3 + 2/4 + 3/5 + ... + 15/17

Summation notation is a mathematical shorthand used to represent the sum of a sequence of terms. It is typically denoted by the Greek letter sigma (Σ), followed by an expression that defines the terms to be summed, along with limits that specify the starting and ending indices. For example, Σ from i=1 to n of a_i indicates the sum of the terms a_1, a_2, ..., a_n.

The index of summation is a variable that represents the position of each term in the sequence being summed. In the expression Σ from i=a to b of f(i), 'i' is the index that takes on integer values from 'a' to 'b'. This index allows us to systematically enumerate each term in the sum, making it easier to express complex series in a concise form.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. In the given sum, the numerators (1, 2, 3, ..., 15) form a simple arithmetic sequence where each term increases by 1. Understanding the properties of arithmetic sequences is essential for identifying patterns and expressing sums in summation notation.