My Favorite Number is 1153

If the maximum power of 5 in \(n!\) is \(k_n\) (For example \(k_{10}=2\) since \(10!=2^8×3^4×5^2×7\)), find the value of \[\displaystyle \sum_{n=1}^{1153}{[k_n×(-1)^{n+1}]}\]


This is one part of 1+1 is not = to 3.

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