# Telescopic 2014

Calculus Level 4

$S=\sum_{r=2}^{2014} \left[(-1)^r \dfrac{r^2+r+1}{r!}\right]$

The value of $S$ is of the form $a+\dfrac{1}{b!}+\dfrac{1}{c!}$ Where $a,b$ & $c$ are integers and $a$ & $b$ are co-prime.

Find $\dfrac{2a+2b+c}{4}$

• Please avoid using Wolfram Alpha or any other CAS.
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