What diverges?

Calculus Level 3

Which of the following series diverges?

A: nZ+n4144n+log4\displaystyle \sum\limits_{n\in\mathbb{Z^+}} \frac{n^4-\frac{1}{4}}{4^n+\log4}

B: nZ+(n2+3n4n5+6)n\displaystyle \sum\limits_{n\in\mathbb{Z^+}} (\frac{n^2+3n}{4n^5+6})^n

C: nZ+5sin(n)+12cos(n)13en\displaystyle \sum\limits_{n\in\mathbb{Z^+}} \frac{5\sin(n)+12\cos(n)}{13e^n}

D: nZ+e(n!)enne\displaystyle \sum\limits_{n\in\mathbb{Z^+}} \frac{e(n!)}{e^n-n^e}

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