Wm C Bauldry 

Dept of Mathematical Sciences
Appalachian State University 

Series of Real Numbers 

A series is generated by summing a sequence of terms. The partial sums of the series are given by . We say the series converges to a limit when the sequence of partial sums converges. Since it's very difficult to tell by inspection when a series converges, we select from a set of convergence tests that increase in power, but also increase in the effort needed for their computation. We must interpret the results of any test to determine what it tells us about the series in question. 

The Series Test Calculator let's us enter the general term , the beginning index , and then have Maple perform the computations by clicking the Do the Tests button. After interpreting the results, then click the Evaluate button to see Maple's answer with a graph of the partial sums and the terms . Compare your results with Maple's. 

Try the Series Test Calculator with series that you know; for example, try the calculator on series with terms given by and  

The Series Test Calculator 

Enter and n0 :=. Now
D'Alembert's Ratio Test:	Cauchy's Root Test:
Raabe's Test:	The Integral Test:
Maple's Results
The Series:

References 

• Convergence tests. From Wikipedia, the free encyclopedia.

 

• Convergence Tests for Infinite Series. From the "Online Mathematics Tutorials" at Harvey Mudd College.

 

• Choosing a Convergence Test for Infinite Series. David J. Manuel, Texas A & M University.

 

• List of Convergence Tests. From Wolfram MathWorld.