I know some applications of mathematical induction, such as D'moivre's theorem and triangular inequality, but I wanted something more, like derivatives, limits or some complex identities to which I could apply mathematical induction.
If anyone knows any material, please indicate :)
How about this one?
Consider a Taylor series
$$ f(x) = \sum_{n=0}^\infty \frac{a_n}{n!} x^n $$
Then for all natural numbers $k$, the $k$'th derivative of $f$ is $$ f^{(k)}(x) = \sum_{n=0}^\infty \frac{a_{n+k}}{n!} x^n $$ with the same radius of convergence.