Question

What is 1!+2!+3!+4!+5!+6!+7!+8!+9!+10!+11!+12!+13!+14!+15!+16!+17! ?

I know that ! means that you multiply all the factors before it(4!=4x3x2x1)This may be wrong so could you please help me???

Answer 1

Answer:

bro the answer you are telling is right

Answer 2

Answer:

Last digit is the remainder when(1!+2!+3!+⋯+33!)33is divided by 10

1!=12!=23!=64!=245!=1206!=720

7!=5040

1!+2!+3!+4!=1+2+6+24=33

What we observed that the unit digit of all factorials starting from 5! upto

33! is 0.

∴The unit digit of the sum(1!+2!+3!+⋯+33!)is 3

⟹(1!+2!+3!+⋯+33!)≡3(mod10)(1)

⟹(1!+2!+3!+⋯+33!)10≡(3)10(mod10)

⟹(1!+2!+3!+⋯+33!)10≡9(mod10)

⟹(1!+2!+3!+⋯+33!)30≡(9)3(mod10)

⟹(1!+2!+3!+⋯+33!)30≡9(mod10)

⟹(1!+2!+3!+⋯+33!)33≡9×33(mod10)using (1)

⟹(1!+2!+3!+⋯+33!)33≡243(mod10)

⟹(1!+2!+3!+⋯+33!)33≡3(mod10)

∴The last (unit) digit of(1!+2!+3!+⋯+33!)33is 3