In order to describe the series with sigma notation, you must first of all write the explicit formula for the terms of the sequence. In the above example the given sequence was {3, 5, 7, 9, ... } which is represented by the explicit formula 2n + 1.
Parentheses, at times, have to be used. Since the explicit formula for the given example was in the form of a binomial, brackets were needed.
There is a big difference between and .
means [(2 x 1) + (2 x 2) + (2 x 3) + (2 x 4) + (2 x 5)] + 1 which equals 30 + 1. Thus, the sum is now 31 as opposed to 35.