I have an inequalities equation that looks like:
$$\sum_{B=1}^n B (\frac{e}{4})^\frac{B}{2} \ge 1$$
Is it possible to solve for n, where n is the upper bound of B (a constant).
I'm currently trying to solve using partial sum series (see below), but it doesn't lead me anywhere after I expanded it.
$$\frac{n(n+1)}{2} (\frac{e}{4})^\frac{B}{2} \ge 1$$
When $n\ge 2$, the third term is $2(\frac e4)^{\frac22}=\frac e2\gt 1$.
For $n=1$, you get $(\frac e4)^{\frac12}\lt 1$... so it's false...