How do you know if a series converges by the intergral test?
When you take the integral using the series as integrand, it converges if the integral worked out to be a number. If it's infinte, the series diverge.
D'Alembert's ratio test, or simply the ratio test, is a way of determining whether certain series converge. It goes like this: to check if a series converges, check the sequence of ratios between consecutive terms. If that sequence converges to something less than 1, then the series converges absolutely. If it converges to something greater than 1, or diverges, then the series diverges. If it converges to 1 exactly, then the test is inconclusive.
You've an exam on series what essential things are there to know integral ratio test root test maclaurin Taylor pseries etc Can someone explain?
Let us call a series S, it is hard to put all the notation we need here, because we do not have the proper characters, but I will try. 1. One type of series is a geometries series. It converges if for the sum q^n where n goes from 0 to inginitye, q is stritclty between -1 and 1. 2. Consider an integer N and a non-negative monotone decreasing function f defined on the unbounded…
The comparison test states that if a series of positive numbers converges, and in another series, each of the corresponding terms is smaller, then it too must converge. Similarly, if a series of positive numbers diverges to infinity, and another series has each of its terms greater than the corresponding terms of the other, then it too diverges.
England in India 1993 = India won 3 test series 3-0. Sri Lanka in India 1994 = Inda won 3 test series 3-0. Zimbabwe in India 2002 = India won 2 test series 2-0. India in Bangladesh 2004 = India won 2 test series 2-0. India in Zimbabwe 2005 = India won 2 test series 2-0. India in Bangladesh 2010 = India won 2 test series 2-0. Australia tour of India 2010 = India won…
An ammeter is connected in series. A voltmeter is connected in parallel. ammeter should always be connected in series instead of parallel becoz it is a low resistance device and we know that resistance is inversly proportional to current so more current will pass through it and if it is connected in parallel than it may get damaged