Question

determine if the series converge or diverge.? : ln (n/(2n+1))

Answer 1

In a converging series the numbers will tend towards 0
In a diverging series the numbers will continue to tend towards plus or minus infinty

Answer 2

One way is to simply substitute the values of n = 1,2,3......and so on and see if the numbers are becoming smaller and tending towards 0 or not

Answer 3

Another way is to observe that the denominator will continue to grow at a rate twice than the numerator and so - the number will keep on becoming smaller

Answer 4

but how to show it.?by using graph or are there any other proof I can show that the series converge or diverge.?

Answer 5

oh you can find the limit of this and prove it that it tends to zero

Answer 6

so the answer is converge right.?

Answer 7

yes

Answer 8

well then..thank you!

Answer 9

no the series doesn't converge since the limit is non-zero. So it diverges by Divergence test