How can I show if these series are convergent or divergent?
∑k = 1∞ cos((k^(3))/(3^(k))
∑k = 1∞ ((-1)^(k))((sin(1/k))/(k))
Appriciate any guidance and a detail explanation.
The first one is pretty easy.
and it is divergent. If it was 0 the test would've been inconclusive. (limit test)
For the second one:
you can see that
and it is decreasing (by drawing the graphic of the function .
We can conclude that it is alternating series which converge.