Question

13
Find the unit digit of 1! + 2!+ 3!+ 4!+......+300!​

Answer 1

Step-by-step explanation:

unit digit would be 5

hope it helps

Answer 2

Answer:

The unit digit of 1! + 2!+ 3!+ 4!+......+300! = 3

Step-by-step explanation:

To find,

The unit digit of 1! + 2!+ 3!+ 4!+......+300!​

Recall the formula

n! = 1×2×3×4×...×n

Solution

1!  = 1

2! = 1×2 = 1!×2 =  2

3! = 1×2×3 = 2!×3 = 6

4! = 1×2×3×4 = 3!×4 = 24

5! = 1×2×3×4×5 =4!×5= 120

6! = 1×2×3×4×5×6 = 5!×6 = 720

From this, we can conclude that all the factorials above 5! are multiples of 5!. Hence all the factorials from 5 and above have unit digit is equal to '0'

That is unit digit of 5!+6!+7!+ ------300! = 0

Hence,

unit digit of 1! + 2!+ 3!+ 4!+......+300!​ = unit digit of (1! + 2!+ 3!+ 4!)

=unit digit of1+2+6+4

=3

∴The unit digit of 1! + 2!+ 3!+ 4!+......+300! = 3

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