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

Key Concepts

Summation Notation

Summation notation is a mathematical shorthand used to represent the sum of a sequence of terms. It typically uses the Greek letter sigma (Σ) to denote the sum, along with an index of summation that indicates the starting and ending values. For example, Σ from i=1 to n of a_i represents the sum of the terms a_1, a_2, ..., a_n.

Index of Summation

The index of summation is a variable that represents the position of each term in the sequence being summed. It is usually denoted by a letter, commonly 'i', and it takes on integer values starting from a specified lower limit to an upper limit. Understanding how to manipulate the index is crucial for correctly expressing sums in summation notation.

Pattern Recognition in Sequences

Pattern recognition in sequences involves identifying a consistent rule or formula that describes the terms of the sequence. In the given sum, recognizing that the numerator increases by 1 and the denominator increases by 1 as well helps in formulating the general term. This ability to discern patterns is essential for accurately expressing sums in summation notation.