- #1
mikbear
- 5
- 0
Hello. I.m struggling to understand how to test for convergent and divergent.
∞
Ʃ (n/(n+1))^(n^2)
n=1
∞
Ʃ (n/(n+1))^(n^2)
n=1
The "Series Test for convergent and divergent" is a method used to determine whether an infinite series, which is a sum of infinitely many terms, converges (approaches a finite limit) or diverges (does not approach a finite limit). It is used in the field of calculus and is an important tool for evaluating the convergence of various mathematical series.
There are several different types of series tests, including the comparison test, the ratio test, the root test, and the integral test. Each test has its own criteria and is used in different situations to determine the convergence or divergence of a series.
The comparison test is used to compare the convergence of one series to another series with known convergence. If the known series converges and the terms of the unknown series are smaller, then the unknown series must also converge. If the known series diverges and the terms of the unknown series are larger, then the unknown series must also diverge.
The ratio test is a test for convergence that compares the ratio of successive terms in a series to a limit. If the limit of the ratio is less than 1, then the series converges. If the limit is greater than 1, then the series diverges. If the limit is equal to 1, then the test is inconclusive and another test must be used.
The integral test should be used when the terms of a series can be written as a continuous function. It compares the convergence of the series to the convergence of an improper integral. If the integral converges, then the series must also converge. If the integral diverges, then the series must also diverge.