Mar 20, 2015 · Prove that $$\sum_ {n=1}^ {\infty} \frac {\sin (n)} { {n}^ {2}}$$ is either absolutely convergent, conditionally convergent or divergent. Note that $$\sin (n) \in [-1,1] \text { for} \left| …

absolute\:convergence\:\sum_{n=1}^{\infty}\frac{\cos(n)}{n^2} absolute\:convergence\:\sum_{n=1}^{\infty}(-1)^n\frac{\sin(n)}{n^2} Show More

Jul 27, 2017 · One can prove that $\sin n$ diverges, using the fact that the natural numbers modulo $2\pi$ is dense. However, the case for $\sin (n^2)$ looks much more delicate since …

In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. …

Feb 18, 2024 · \sin(n\pi/2) = \frac{e^{in\pi/2} - e^{-in\pi/2}}{2i} = \frac{i^n - (-i)^n}{2i} = \frac 12 (i^{n-1} + (-i)^{n-1}) $$

I need to see whether the following series converges or diverges: $\frac{\sin^2(n)}{n}$, with n from 1 to infinity. The problem is that sin is defined on complex numbers, so this time sin can take …

Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, …

In basic trigonometry computes sine, cosine, tangent, and their reciprocal. Calculates arcsin, arccos, and arctan values inside inverse trigonometric equations. Trigonometric identities …

The Sequence a_n = sin (n)/n Converges or Diverges Two Solutions with Proof If you enjoyed this video please consider liking, sharing, and subscribing....more.

结论： \sin {n^2} 这个数列不仅发散，而且它的全体极限点（也就是聚点）为 [-1,1]