Boy, that escalated quickly (Fixed)

Let n n be a positive integer satisfying 2 n + 4 = 8 2n+4=8 . Compute x = 1 10 n x ( x ! + x n ) \displaystyle \sum_{x=1}^{10} n^x (x! + x^n) .


The answer is 3912873140.

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1 solution

Julian Yu
Dec 3, 2018

Obviously n = 2 n=2 . So the summation becomes x = 1 10 2 x ( x ! + x 2 ) \displaystyle \sum_{x=1}^{10} 2^x (x! + x^2) , which is 4 + 24 + 120 + 640 + 4640 + 48384 + 651392 + 10338304 + 185836032 + 3715993600 = 3912873140 4 + 24 + 120 + 640 + 4640 + 48384 + 651392 + 10338304 + 185836032 + 3715993600=\boxed{3912873140} .

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