$(1\times 2\times 3\times 4) + (2\times 3\times 4\times 5)+\ldots+ (47\times 48\times 49\times 50) = \ ?$

You may use a calculator for the final step of your working.

The answer is 56377440.

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Since it appears simple enough to brute force using computer, that is precisely what I did:

While solving, I didn't notice the similarity with the binomial coefficients $\binom{n}{4}$ .