Hi everyone,

I’ve been dealing with some sequence problems where I need to check if the sequence is increasing or decreasing. Usually, I just look at u_{n+1} — u_n, but for some complex functions, it gets messy.

I’ve been trying to use the derivative f'(x) (treating n as x) to check for monotonicity. It makes things much easier, but I’m a bit worried about the domain. Since f'(x) is for x ∈ R and a sequence is only defined for n ∈ N*, is this approach always rigorous? Or are there cases where this might fail?

For instance, if I have u_n = 2^n — an, what’s the best way to find the range of a so that the sequence is strictly increasing? Should I stick to the derivative or is there a better "competitive programming" way to handle this?

Any advice would be great. Thanks!