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S=\sum_{n=0}^{M} \frac{M ! x^{n}}{n !(M-n) !}
\]
Where \( M \) and \( N \) are very large numbor (about \( \left.10^{20}\r](https://media.cheggcdn.com/study/f0b/f0b9c70a-0df8-43e7-9dd4-22d3256e7df0/image)
Expert Answer
we can use Stirling's appropriation for S. Stirling's approximation states that for large values of n, n! is approximately equal to . Using this approximation, we can rewrite the express for S as: Taking the natural logarithm of both side we get: