Monthly Archives: September 2016

distinguishing between convergent series and divergent series

In this blog, we will learn how to distinguish between series that converge and series that diverge.

First, series is a sum of a sequence; for instance, {1+2+3+4+……}. We can say that a series converge if the limit of the sum equals a finite number, such as 0, 1, 2, or any number, while a series diverge if the limit of the sum does not equal a finite number, such as infinity; for example, limit the natural numbers as n approaches infinity, {1 + 2 + 3 + 4+……}equals infinity, wich means the series of the natural numbers diverge.

 

 

In this blog, I will demonstrate how to distinguish when a sequence converges or diverges.

Convergence means a sequence is Approaching a certain number, such as 0, 1, or any number; for example, the limit of this sequence {1,-1/2, 1/3, -1/4 , 1/5. ……}  is approaching 0; therefore we can say that the limit converges to 0

However, if we did not find that a sequence approaches a certain number, we can say that the sequence diverges.