Factorials

Number Theory Level 2

Find the last 2 digits in the sum

1 ! + 2 ! + 3 ! + ⋯ + 2017 ! . 1! + 2! + 3! + \cdots + 2017! .


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


The answer is 13.

View wiki
Christopher Ho by Christopher Ho , 17, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Christopher Ho
Mar 18, 2017

We observe the last two digits of the first few factorials

1! = 1

2! = 2

3! = 6

4! = 24

5! = 20

6! = 20

7! = 40

8! = 20

9! = 80

We can ignore the other factorials; they will each end in 00 because they can each be expressed as 100 times some value. Adding these up gives us the number 213, whose last two digits are 13

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Same way ^-^

Andrea Virgillito - 4 years, 2 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...