# How to address an inequality having the amount of factorials and also powers

In previous question, I asked just how one would certainly streamline the list below formula for the instance where the variables are large:

$\sum\limits^{k}_{i=m}(N-i)^{k-i}(\frac{1}{N})^k\frac{k!}{(k-i)!i!} \leq a$

This solution was primarily to make use of an estimate like Stirling is formula. Having actually applied this with some code, it still takes also lengthy to locate the maximum value of N to make sure that the inequality applies. Consequently, I require a straight remedy for N. So the new inquiry is, just how would certainly you deal with addressing this formula for N?

(Some simplifications serve, yet I would love to have it as exact as feasible. The values this formula will certainly be made use of for are done in the 100,000 - 1,000,000 array, other than $m$, which remains in the 100s array.)

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2019-05-18 20:27:18
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