All the factorials you know

Number Theory Level 2

If n ≥ 5 n\geq 5 , find the last digit of 1 ! + 2 ! + 3 ! + ⋯ + n ! 1! + 2! + 3!+ \cdots + n! .

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


The answer is 3.

View wiki
Rishabh Sood by Rishabh Sood , 20, India

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

Ashish Menon
Aug 7, 2016

Any value of n ! n! suchat that n ≥ 5 n \geq 5 would have 0 as in its unit place.
So, the units digit of the summation would be just the units digit of the summation of the units digit of 1 ! , 2 ! , 3 ! , 4 ! 1!, 2!, 3!, 4! which is 1 + 2 + 6 + 4 = 1 3 = 3 1+2+6+4 = 1\color{#3D99F6}{3} = \color{#20A900}{\boxed{3}} .

7 Helpful 0 Interesting 0 Brilliant 0 Confused

You have a typo in your solution. You should have n ≥ 5 n \geq 5 instead of n > 5 n > 5 .

Jesse Nieminen - 4 years, 10 months ago

Log in to reply

Thanks! I corrected the typo

Ashish Menon - 4 years, 10 months ago

Doesn't change the answer, but 4! Is 24, not 4.

Dom Kroupa - 4 years, 10 months ago

Log in to reply

I have mentioned unit's digit summation

Ashish Menon - 4 years, 10 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...