Telescopic 2014

Calculus Level 4

S=r=22014[(1)rr2+r+1r!]S=\sum_{r=2}^{2014} \left[(-1)^r \dfrac{r^2+r+1}{r!}\right]

The value of SS is of the form a+1b!+1c!a+\dfrac{1}{b!}+\dfrac{1}{c!} Where a,ba,b & cc are integers and aa & bb are co-prime.

Find 2a+2b+c4\dfrac{2a+2b+c}{4}

  • Please avoid using Wolfram Alpha or any other CAS.
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