Question

find the unit digit in the sum of factorials from 1 to 10, that is 1!+2!+3!+4!+...........+10!

Answer 1

from 5! to 10! contains product of 5 and 2 so unit place is 0(zero)
1! =1
2!= 2
3!= 6
4!= 25
5! =120
sum of unit place of given expression = 1 +2 +6 +5 +0 = 14
unit place will be 4

Answer 2

Answer:

The required result is 13.    

Step-by-step explanation:

Given : Expression $1!+2!+3!+4!+...........+10!$

To find : The unit digit in the sum of factorials from 1 to 10?

Solution :

We expand all the factorial,

$1!=1$ (unit digit 1)

$2!=2\times 1=2$ (unit digit 2)

$3!=3\times 2\times 1=6$  (unit digit 6)

$4!=4\times 3\times 2\times 1=24$ (unit digit 4)

$5!=5\times 4\times 3\times 2\times 1=120$ (unit digit 0)

$6!=6\times 5\times 4\times 3\times 2\times 1=720$ (unit digit 0)

$7!=7\times 6\times 5\times 4\times 3\times 2\times 1=5040$ (unit digit 0)

$8!=8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=40320$ (unit digit 0)

$9!=9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=362880$ (unit digit 0)

$10!=10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=3628800$ (unit digit 0)

Now, The sum of unit digit of factorials from 1 to 10 is

$1+2+6+4+0+0+0+0+0+0=13$

Therefore, The required result is 13.