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## Homework Statement

Solving an exercise I found myself with this problem: the solution ##c## needs to verify both ##\sum_{k=1}^c n\lambda^k\frac{e^{n\lambda}}{k!}\leq \alpha## and ##1-\sum_{k=1}^{c+1} n\lambda^k\frac{e^{n\lambda}}{k!}\geq \alpha##.

Can an equation like this be solved for c?

## Homework Equations

## The Attempt at a Solution

An inversion of the inequality didn't work because it vanishes ##\alpha##, I don't think there is an explicit form for the solution, but I've failed in finding an argument to explain why.

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