Jbreezy said:Homework Statement
Ʃ (-1)^n [ n+ln(n) / n-ln(n)] from n = 2 to infinity.Homework Equations
I looked at the limit first because I thought lnn was very slow function. n would go faster.
The Attempt at a Solution
limit n --> ∞ [ n+ln(n) / n-ln(n)] = 1 so it diverges.
Limit is not 0 so it violates the one of the conditions? OK ? OR wrong?
Thanks,
Jbreezy said:Homework Statement
Ʃ (-1)^n [ n+ln(n) / n-ln(n)] from n = 2 to infinity.
Homework Equations
I looked at the limit first because I thought lnn was very slow function. n would go faster.
The Attempt at a Solution
limit n --> ∞ [ n+ln(n) / n-ln(n)] = 1 so it diverges.
Limit is not 0 so it violates the one of the conditions? OK ? OR wrong?
Thanks,
An alternating series is a series in which the terms alternate in sign, such as (-1)^n or (-1)^(n+1). This means that every other term in the series is positive and the remaining terms are negative.
To solve equations involving alternating series, you can use the alternating series test or the absolute convergence test. These tests help determine whether the series converges or diverges. If the series converges, you can then use other methods such as the ratio or root test to find the exact value.
The alternating series test states that if the terms of an alternating series decrease in absolute value and approach 0, then the series converges. This means that the sum of the series approaches a finite value as the number of terms increases.
The absolute convergence test states that if the absolute value of a series converges, then the original series also converges. This test is useful for determining the convergence of series with alternating signs.
No, the alternating series test can only be used for certain alternating series that meet the conditions of the test. For example, the series must have alternating signs and decreasing terms that approach 0. If these conditions are not met, then other tests or methods must be used to determine the convergence of the series.