Question

Dirichlet's Test, 2 examples.

Answer 1

Series: \(\color{#000000 }{ \displaystyle \sum_{t=s}^\infty \frac{\cos t}{\ln t} }\)

Contains:
(1) General Theory of Dirichlet's Test
(2) Derivation of partial sum of the geometric series

Purpose:
(!) Proof that the series converges, by Dirichlet's Test.

(This is the final version, with more precise wording)

Answer 2

Series: \(\color{#000000 }{ \displaystyle \sum_{t=s}^\infty t^{-0.0001}\sin t }\)

Purpose:
(!) Proof that the series converges, by Dirichlet's Test.

(I don't repeat the theory part of the geometric series and Dirichlet's Test in document #2, and additionally I am informing you that THIS is the final version (of doc 2), with more precise wording)