genevievelily said:Homework Statement
Is the following convergent or divergent?
ln(2(n+1))-ln(2n)
Homework Equations
comparison test
The Attempt at a Solution
I put it into the form ln(1+(1/n)), but I don't understand what to use as Bn for the comparison test. (which is what wolfram alpha uses)
A convergent series is a mathematical series in which the terms get closer and closer to a specific value as the number of terms increases. This specific value is called the limit.
A divergent series is a mathematical series in which the terms do not approach a specific value as the number of terms increases. Instead, the series either grows infinitely large or oscillates between different values.
One way to determine if a series is convergent or divergent is by using the comparison test, where the given series is compared to a known convergent or divergent series. Another way is to use the ratio test, which compares the ratio of consecutive terms to a limit.
Convergent and divergent series have many real-world applications, such as in finance, physics, and computer science. For example, the calculation of compound interest involves a convergent series, while the motion of a pendulum can be modeled using a divergent series. In computer science, the convergence or divergence of a series can determine the efficiency and accuracy of algorithms.
One common misconception is that a divergent series must have infinitely large values. However, a divergent series can also oscillate between different values. Another misconception is that a convergent series must approach a finite value. Some convergent series, known as conditionally convergent series, approach a specific value only when certain conditions are met.