Convergence and divergence refer to the behavior of a series as the terms approach infinity. A convergent series is one where the terms approach a finite limit, while a divergent series is one where the terms do not approach a finite limit.
The convergence or divergence of a series can be determined by evaluating the limit of the terms as n approaches infinity. In the case of cos(1/n), the limit will approach 1, indicating that the series converges.
Yes, the Ratio Test can be used to prove the convergence of cos(1/n). The ratio of successive terms in the series will approach 1, indicating that the series converges.
There is no specific method for finding the sum of a series like cos(1/n). However, the sum can be approximated by adding a finite number of terms and using mathematical techniques like the Midpoint Rule.
The convergence of cos(1/n) can be applied in fields like physics and engineering to model situations where a quantity approaches a limit. It can also be used in financial mathematics to calculate the present value of an infinite stream of payments.