The way we approach this problem is by first deciding which test we should use to determine whether it converges or not. Then we apply the test, and we see if it responses with the test or not. Finally, by the test, we can know if it converges or diverges.
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.
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