HallsofIvy said:
You can type in LaTeX if you'd like: Introducing LaTeX Math Typesetting - https://www.physicsforums.com/showthread.php?t=8997joellecool said:
A series is the sum of a sequence of numbers, while a sequence is a list of numbers in a specific order. In other words, a series is the result of adding the terms of a sequence.
To find the sum of a series, you can use the formula S = a/(1-r), where a is the first term and r is the common ratio between the terms in the series. Alternatively, you can use the partial sum formula, Sn = (a(1-r^n))/(1-r), where n represents the number of terms in the series.
In an arithmetic series, each term is found by adding a constant value to the previous term. In a geometric series, each term is found by multiplying the previous term by a constant value.
A series is convergent if the limit of the partial sums approaches a finite number as the number of terms in the series approaches infinity. A series is divergent if the limit does not approach a finite number. For a sequence, you can use the limit comparison test or the ratio test to determine convergence or divergence.
One example of a series is the Fibonacci sequence, where each term is the sum of the two previous terms (1, 1, 2, 3, 5, 8, 13, 21, ...). An example of a geometric series is the infinite sum of 1/2 + 1/4 + 1/8 + 1/16 + ... which converges to 1.