No, you don't know that! You only know that the limit is 0.rcmango said:Homework Statement
n = 1 E infinity (n * sin (1/n))
Homework Equations
geometric series test?
The Attempt at a Solution
It looks like a geometric series.
i know that sin 1/n = 0 by squeeze theorem.
But none of your terms is n* 0 so that is irrelevant.n * 0 will always be 0.
No!am i on the right track, please help.
rcmango said:Okay, thanks Dick, you limit is 1.
i could use the comparison test, compare to 1/n
divide an / bn and get 1 by the nth term series. Thus diverging because it doesn't = 0.
thats what i made out of it. thanks alot.
A series is a sequence of numbers that are added together in a specific order.
A series converges when the sum of its terms approaches a finite value as the number of terms increases. In other words, the series gets closer and closer to a specific number as more terms are added.
To determine if a series converges, we can use various tests such as the ratio test, the root test, or the comparison test. These tests compare the given series to known convergent or divergent series to determine its behavior.
A series diverges when the sum of its terms does not approach a finite value as the number of terms increases. In other words, the series does not have a specific sum and can continue to increase or fluctuate indefinitely.
Series convergence or divergence plays a crucial role in various scientific fields, such as physics, engineering, and economics. For example, in physics, series convergence is used to model physical phenomena and make predictions. In economics, series convergence is used to analyze economic trends and make financial predictions. In engineering, series convergence is used to design and optimize systems and structures.