- #1
Dissonance in E
- 71
- 0
Homework Statement
infinity
SIGMA sqrt(n) / ((n^2)(ln(n))
n = 2
Homework Equations
The Attempt at a Solution
Could i beat this into a p-series perhaps?
You can't "beat" it into a p-series, but you can compare it to a convergent p-series.Dissonance in E said:Homework Statement
infinity
SIGMA sqrt(n) / ((n^2)(ln(n))
n = 2
Homework Equations
The Attempt at a Solution
Could i beat this into a p-series perhaps?
A p-series is a mathematical series in the form of ∑ np, where p is a constant and n ranges from 1 to infinity. It is a type of infinite series, meaning it has an infinite number of terms.
A p-series will converge if the value of p is greater than 1. If p is less than or equal to 1, the series will diverge. This can be determined by using the p-series convergence test, which states that if the limit of np as n approaches infinity is greater than 1, the series will converge. Otherwise, it will diverge.
Yes, you can create your own p-series by choosing a value for p and plugging it into the formula ∑ np. However, not all p-series will converge. It is important to use the p-series convergence test to determine if your series will converge or diverge.
Some examples of p-series include ∑ 1/n, which is known as the harmonic series and diverges, and ∑ 1/n2, which is known as the Basel problem and converges to π2/6.
P-series convergence is important because it allows us to determine whether an infinite series will have a finite sum (converge) or an infinite sum (diverge). This has applications in various fields such as physics, engineering, and economics. Additionally, understanding p-series convergence can help us understand the behavior of other types of infinite series.