Mathematics Post Does the following sequence an=cosn/n^2 converge, or does it diverge? Find the limit if it is a convergent sequence. ByMeruprastaar 2022-04-282022-05-02Write a Comment on Does the following sequence an=cosn/n^2 converge, or does it diverge? Find the limit if it is a convergent sequence. Share Table of Contents Toggle Does the following sequence a_n=\frac{cos\ n}{n^2} converge, or does it diverge? Find the limit if it is a convergent sequence. Explain | an=cosn/n^2a_n=\frac{cos\ n}{n^2} Recall that −1 ≤ cos(n) ≤ 1Hence\frac{-1}{n^2}\leq \frac{cos\ n}{n^2}\leq\frac{1}{n^2}Now since \lim_{n\rightarrow \infty}\frac{-1}{n^2}=\lim_{n\rightarrow \infty}\frac{1}{n^2}=0we conclude, by the Sandwich Principle, that the sequence {a_n} converges to the same limit:\lim_{n\rightarrow \infty}a_nKeywordsconvergence of sequence examplesconvergence of sequence and series Does the following sequence a_n=\frac{cos\ n}{n^2} converge, or does it diverge? Find the limit if it is a convergent sequence. Explain | an=cosn/n^2 a_n=\frac{cos\ n}{n^2} Recall that −1 ≤ cos(n) ≤ 1 Hence \frac{-1}{n^2}\leq \frac{cos\ n}{n^2}\leq\frac{1}{n^2} Now since \lim_{n\rightarrow \infty}\frac{-1}{n^2}=\lim_{n\rightarrow \infty}\frac{1}{n^2}=0 we conclude, by the Sandwich Principle, that the sequence {a_n} converges to the same limit: \lim_{n\rightarrow \infty}a_n Keywords convergence of sequence examples convergence of sequence and series Share Related Geometrical view for square root of 2 by Baudhayana's value square root of 2 by Baudhayana | Square Root of 2, by Baudayana| baudhayana baudhayana theorem baudhayana sulba sutra about baudhayana | MeruPrastaar
Test The Following Series 1/3+1.2/3.5+1.2.3/3.5.7+…∞ 2022-05-042022-05-10 Mathematics Sequence and series गणित
Discuss the nature of the series 1/1.2 +1/2.3 + 1/3.4 + 1/4.5 … Or Discuss the Convergency of the series 1/1.2 +1/2.3 + 1/3.4 + 1/4.5 … Or test the Convergence of the series 1/1.2 +1/2.3 + 1/3.4 + 1/4.5 … 2022-03-312022-05-02 Mathematics Post
Give an example of a series that is conditionally convergent (that is, convergent but not absolutely convergent). solved problems in calculus Absolute and Conditional Convergence 2022-04-172022-05-02 Mathematics Post
