Determine convergence of \sum_{n=1}^\infty(\cos\frac{2}{n}-\cos\frac{4}{n})

Bradlee Hooper

Bradlee Hooper

Answered question

2022-02-28

Determine convergence of
n=1(cos2ncos4n)

Answer & Explanation

avalescogzw

avalescogzw

Beginner2022-03-01Added 5 answers

The result follows from the Addition Law for Cosines.
We have cos(x+y)=cosxcosysinxsiny and
cos(xy)=cosxcosy+sinxsiny. Subtract. We get
cos(xy)cos(x+y)=2sinxsiny
Let xy=2n and x+y=4n. Solve for x and y. We get x=3n and y=1n

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