Question

PLEASE HELP 30 POINTS
1(1!)+2(2!)+3(3!)+...100(100!)=?

Answer 1

Answer: hello sorry I need the points

Explanation:

Answer 2

A more general result:

`1\cdot1!+2\cdot2!+\cdots+(n-1)\cdot(n-1)!+n\cdot n!=(n+1)!-1`

Why is this true?

On the left side,

`1\cdot1!=(2-1)\cdot1!=2\cdot1!-1\cdot1!=2!-1!`

`2\cdot2!=(3-1)\cdot2!=3\cdot2!-1\cdot2!=3!-2!`

`3\cdot3!=(4-1)\cdot3!=4\cdot3!-1\cdot3!=4!-3!`

and so on. Adding will lead to cancellation of all terms in the middle, leaving you with
`(n+1)!-1`.

Then when
`n=100`, the value of the sum is
`101!-1`.