The functional series is given by;$$\sum_{j=0}^\infty \frac{\sin(jx)}{(2+x^2)^j} $$ I believe that for this question I should be using the Weierstrass M-Test. So far I have $$\frac{\vert \sin(jx)\vert}{\vert(2+x^2)^j\vert} \le \frac{1}{\vert (2+x^2)^j\vert} $$ but I am not really sure where to go from here, any help would be much appreciated!
2026-03-28 02:04:36.1774663476
Determine whether the functional series is uniformly convergent
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Hint: $\qquad\dfrac1{|(2+x^2)^j|}=\dfrac1{(2+x^2)^j}\le\dfrac1{2^j} $, and the latter series converges. So ...