Question

Does the ratio test also helps us to identify where does the series converges or Is it that it is only a test for convergence and divergence?

Answer 1

Both

Answer 2

it tells you convergence, divergence, absolute convergence or if it equals 1 it's an inconclusive test try a simpler one

Answer 3

For example I am doing a test of 1/n! and by ratio test I got the limit of a_(n+1)/a_(n) as o which is clearly less than 1, so it is convergent but does it means that it is convergent at 0

Answer 4

no...it's just convergent..the number doesn't matter

Answer 5

So it doesnot provide me the information on where it converges then..........

Answer 6

no...geometric series, integral tests, harmonic series and power series are the only series tests that will provide you an actual sum of where it converges to. For example, the geometric series if absolute value of r < 1 then it will converge to a/1-r. When you get into more in depth series such as the ratio test, the numbers can be awful. It will usually just ask you if it is convergent or divergent, or if it's absolute convergent or conditional convergent or divergent

Answer 7

Thanks sonofa_nh My knowledge on Sequence and series is awfully weak.

Answer 8

it's rather tedious and i understand completely

Answer 9

Which book do u use to study it?