Find the remainder when `1!+2!+3!+4!++n !` is divided by 15, if `ngeq5.`

Answer

3

Explanation

Let,
`N=1!+2!+3!+4!+5!+6!+..+n!`
`implies (N)/(15)=(1!+2!+3!+4!+5!+..+n!)/(15)`
`=(1!+2!+3!+4!)/(15)+(5!+6!+..+n!)/(15)`
`=(33)/(15)`+integer (as 5!,6!,.. Are divisible by 15)
Hence , remainder is 3.