tmt said:I have this limit:
$$\sum_{k = 1}^{\infty} {(\frac{e }{3})}^{k}$$
Which method can I use to find if it converges or diverges?
A series limit problem involves determining whether a series, or a sequence of numbers added together, converges (approaches a finite value) or diverges (has no finite value) as the number of terms increases.
To find the convergence or divergence of a series, you can use various tests such as the comparison test, ratio test, or integral test. These tests compare the given series to a known convergent or divergent series and determine the behavior of the given series.
A convergent series has a finite sum as the number of terms approaches infinity, while a divergent series does not have a finite sum. In other words, a convergent series approaches a specific value, while a divergent series either increases or decreases without any bound.
Yes, a series can have both convergent and divergent parts. This is known as a conditionally convergent series. In this case, the overall behavior of the series is determined by the divergent part.
The results of a series limit problem can be applied in various real-life scenarios, such as in finance, physics, and engineering. For example, the convergence or divergence of a series can help determine the stability of a financial investment or the behavior of a physical system over time.