Sum of factorials

Number Theory Level 3

Find the last 2 digits of:

∑ n = 0 100 n ! \large{\displaystyle \sum_{n=0}^{100}n!}


The answer is 14.

Irvan Ary Maulana Nugroho by Irvan Ary Maulana Nugroho , 20

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1 solution

Matteo Monzali
Jun 5, 2016

You only need to calculate ∑ x = 0 9 x ! \sum _{ x=0 }^{ 9 }{ x! } because the factorials from 10 ! 10! to 100 ! 100! have two zeros at the end and so they don't influence the result.

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