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Stolz–Cesàro array limit

  1. Oct 7, 2016 #1
    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. jcsd
  3. Oct 7, 2016 #2


    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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