Find the last two digits of the following sum: $$5! + 10! + 15! + \cdots + 100!$$
+98 We know all factorials 10 and afterwards end in 00 (as there are two factors of 5 and enough factors of 2s), so it is really 5! which counts. This ends in 20, so the last two digits of the described following sum is clearly 20.
Answer:20
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