# Sum outta nowhere!

Calculus Level 5

$\large{\displaystyle \sum_{k=1}^{\infty}\frac{(-1)^{k}k^{2}( \ln(7))^{k}}{\Gamma(k)}}$

If the value of above summation equals $\large{\frac{A}{B}\left(-(\ln 7)^{C}+D (\ln 7)^{E}-(\ln 7)^{F}\right)} .$

Find the six digit number $$\overline{ABCDEF}$$.

Details And Assumptions:

• $$A,B,C,D,E,F$$ are positive integers not all distinct.

• $$C<E<F$$

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