# Stolz–Cesàro array limit

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1. Oct 7, 2016

### LazuRazvan

1. The problem statement, all variables and given/known data
hello, i have to find the limit of the next array

(xn)=(cos (π/n+1) + cos (π/n+2) + .....+ cos ( π/2n))/n
when n goes to infinity.

2. Relevant equations
I was told to apply stolz cesaro and that is where i ended up :
the limit is :

limit of cos ( π/2n+1) + cos (π/2n+2) -cos (π/n+1)

3. The attempt at a solution
How i finish this ?

2. Oct 7, 2016

### Staff: Mentor

What you wrote in the first term was $\cos(\frac{\pi}{n} + 1)$, and similar in the other two terms. Is that what you intended?
Same comment as above.

Also, to apply Stolz-Cesaro (https://en.wikipedia.org/wiki/Stolz–Cesàro_theorem), you need to use it with another sequence. What's the other sequence you are using?

Last edited: Oct 7, 2016
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