Question

If n=1!+2!+3!+-----+2010! What is unit digit for n

Answer 1

Step-by-step explanation:

1+2×1+3×2×1+4×3×2×1

=1+2+6+24

33. unit digit=3

Answer 2

unit digit of n will be 3   if n=1!+2!+3!+-----+2010!

Given:

• n=1!+2!+3!+-----+2010!

To Find:

• Unit digit of n

Solution:

• p! = p . (p - 1). (P-2)... (3)(2)(1)
• ! means factorial
• p! means product of all natural numbers from p to 1.
• In any product of numbers if 2 and 5 both are there then unit digit is 0.

n=1!+2!+3!+-----+2010!

Step 1:

Understand that all the numbers from 5!  onwards has 5 and 2 as factors hence unit digit would be 0

Hence unit digit of n would be same as of

1!+2!+3!+ 4!

Step 2:

Calculate the value of 1!+2!+3!+ 4!

1 + 2 + 6 + 24

= 33

Hence unit digit of n will be 3

unit digit of n will be 3   if n=1!+2!+3!+-----+2010!