Series Tips & Reminders

First of all, what is a series? Isn't it the same thing as a sequence?

Tips for Doing Series Problems

No, though they are related, a series is very different from a sequence.An infinite series is the sum of an infinite sequence of numbers.

Remember:The formula a/(1 - r) for the sum of a geometric series of the form ar^n applies ONLY when the summation index begins with n = 0.

The Divergence Test ONLY can tell us if the series diverges. Just because the limit does equal zero does NOT necessarily mean that the series converges.

Reindexing a Series:To raise the starting value of the index h units, replace the n in the formula by n - h.To lower the starting value of the index h units, replace the n in the formula by n + h.

Here is an illustration of how an infinite amount of values can converge to a finite number when added together.

Here, the fractions converge to fill the whole square, which represents a value of 1.

Series being evaluated using the p-series test converge ONLY if p > 1.If p =1 or p < 1, the series diverges.

Still having trouble deciding which test to try first? Watch the video to the right...maybe it will help!

Remember: When using Comparison or Limit Comparison, you should still say by which test the "known series" converges or diverges.