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teng125
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Determine whether the following series converge or diverge.
(infinity) sum (k=1) (k+4)/(k^2 - 3k +1)
pls help...
thanx...
(infinity) sum (k=1) (k+4)/(k^2 - 3k +1)
pls help...
thanx...
That makes no sense. If you "divide everything by k", by which I presume you mean divide each term in both numerator and denominator by k, you get [itex]\frac{1+ \frac{4}{k}}{k- 3+\frac{1}{k}}[/itex].teng125 said:i try to divide everything by k and let k to infinity and finally got infinity which is diverges
When a series is said to converge, it means that the sum of its terms approaches a finite value as the number of terms increases. Conversely, a series is said to diverge when its sum approaches infinity as the number of terms increases.
There are several tests that can be used to determine the convergence or divergence of a series, such as the Ratio Test, Comparison Test, and the Integral Test. These tests involve evaluating the behavior of the terms in the series as the number of terms increases.
No, a series cannot converge and diverge at the same time. It can only have one of these two outcomes. However, there are some series that are considered to be conditionally convergent, meaning that it converges when certain conditions are met but diverges when those conditions are not met.
Determining the convergence or divergence of a series is important in mathematics and science, as it helps us understand the behavior and properties of different functions and equations. It also allows us to make predictions and draw conclusions about the behavior of a system or phenomenon.
No, not all series can be easily classified as either convergent or divergent. Some series may require more complex or specialized tests to determine their convergence or divergence. In some cases, the convergence or divergence of a series may be impossible to determine definitively.