How to compute $1 \times 2 \times 3 \times 4 + 3 \times 4 \times 5 \times 6 + ... + 97 \times 98 \times 99 \times 100$ How to compute $S = 1 \times 2 \times 3 \times 4 + 3 \times 4 \times 5 \times 6 + ... + 97 \times 98 \times 99 \times 100$
Was thinking $\frac{S}{24} = {4\choose 4} + {6\choose 4} + {8\choose 4} + ... + {100\choose 4}$ but how do I sum this up?

I don't have reputation for comment. so trying to answer here.
${S_n= (2n-1)(2n)(2n+1)(2n+2)}$, simplifying it.

*

*${S_n = (2n) \cdot (4n^2-1) \cdot (2n+2)}$,

*${S_1+S_2+S_3+S_4= 24+360+1680+5040=7104}$

*Simple program gives sum till ${100 = 33211999680 }$
