Type and execute this line before begining the project below. There are many occasions where a series is closely related to an integral. In these cases,the integral will converge or diverge if and only if the corresponding sum converges or diverges. This result is calle the Integral Test. Remember a sequence is function defined on the domain of natural numbers.
Lets look at an example.
Here is a function, the sequence it defines, and a plot of the sequence and function. If curve encloses infinite area then so does the larger step function because at all times it is greater than or equal to the curve. On the other hand, if the curve encloses a finite area, then so does the smaller step function. However, the upper step function is the lower one shifted one unit to the right. Consequently, the series converge or diverge as the integral does.