cmi-entrance 2015 Q18*

cmi-entrance · India · pgmath 10 marks Number Theory Irrationality and Transcendence Proofs
Let $$f(x) = \sum_{n \geq 1} \frac{\sin\left(\frac{x}{n}\right)}{n}$$ Show that $f$ is continuous. Determine (with justification) whether $f$ is differentiable.
Let
$$f(x) = \sum_{n \geq 1} \frac{\sin\left(\frac{x}{n}\right)}{n}$$
Show that $f$ is continuous. Determine (with justification) whether $f$ is differentiable.