Find the remainder when 1!+2!+3!+...+15! is divided by 15

Find the remainder when 1!+2!+3!+...+15! is divided by 15

We already know that,

n! = 1 × 2 × 3 × ... × n

15 = 3 × 5

∵ 5! = 1 × 2 × 3 × 4 × 5 is divisible by 15

⇒ n! { n ≥ 5 } can be divided by 15.

Now, according to our question,

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

⇒ Remainder =

⇒ 2 rem 3

⇒ Remainder = 3

The Remainder is 3

answer: 34rtyj,jkhtyetwrhyjeuiejnbhdfknbkguxfrbhkfdbjvkmbd,kvbsd.kxjvbhjnfbgjxdfn

step-by-step explanation: