# Dual summation

Calculus Level 4

$\sum_{i=1}^{1728}(i)(i-1727)=N$ and $\sum_{e=1}^{\infty}\frac{6e+7}{7^{e+1}(e)(e+1)}=M$ . Then find the remainder when $$\frac{MN+1}{M}$$ is divided by $$1000$$.

Problem is original.

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