How do you determine the convergence or divergence of Sigma 1/ncosnpi from [1,oo)?
1 Answer
Dec 29, 2016
Explanation:
First, we note that
This series satisfies Leibniz' criteria as:
lim_n 1/n = 0
1/n > 1/(n+1)
so the series is convergent.
To determine the sum, let's consider a geometric series of ratio
This series is absolutely convergent and so it can be integrated term by term:
This equation holds for every