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?LazuRazvan said:Homework Statement
hello, i have to find the limit of the next array
(xn)=(cos (π/n+1) + cos (π/n+2) + ...+ cos ( π/2n))/n
Same comment as above.LazuRazvan said:when n goes to infinity.
Homework 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)
LazuRazvan said:The Attempt at a Solution
How i finish this ?
The Stolz-Cesàro array limit, also known as the Stolz-Cesàro theorem, is a mathematical theorem that states the limit of a sequence can be calculated by taking the ratio of the difference between consecutive terms and the difference between consecutive terms of a related sequence. This theorem is useful in determining the convergence of infinite series.
The Stolz-Cesàro array limit is used to calculate the limit of a sequence that is difficult to evaluate directly. By taking the ratio of differences between terms, it can simplify the calculation and provide a more accurate result.
The Stolz-Cesàro array limit is a specific application of the more general Cesàro mean. While the Stolz-Cesàro array limit uses the ratio of differences between consecutive terms, the Cesàro mean can use different operations, such as the arithmetic mean or geometric mean, to calculate the limit of a sequence.
The Stolz-Cesàro array limit has applications in various fields, including physics, engineering, and finance. For example, it can be used to determine the convergence of infinite series in physics equations or to analyze the stability of a control system in engineering. It can also be used to calculate the average rate of return in financial investments.
While the Stolz-Cesàro array limit is a useful tool in determining the limit of a sequence, it cannot be applied to all sequences. It is only valid for sequences that satisfy certain conditions, such as a strictly increasing or decreasing sequence. It also cannot be used when the original sequence has a finite limit. In these cases, other methods may need to be used to calculate the limit.