But The Numbers Get So Big!

Number Theory Level 2

Find the unit digit of 1 ! + 2 ! + ⋯ + 99 ! + 100 ! 1!+2!+\cdots+99!+100! .

Notation :
! ! denotes the factorial notation. For example, 8 ! = 1 × 2 × 3 × ⋯ × 8 8! = 1\times2\times3\times\cdots\times8 .

0 3 4 5

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Shiv Kumar by Shiv Kumar , 32, India

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1 solution

Shiv Kumar
Mar 28, 2016

since after 4 ! 4! every term have unit place 0, so we have to calculate up to 1 ! + 2 ! + 3 ! + 4 ! 1!+2!+3!+4! that is 1 + 2 + 6 + 24 1+2+6+24 or 33, so unit digit is 3 \boxed3 .

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