Remainder when 1·1! + 2·2! + ... + 12·12! is divided by 13

[Young wolf]

Homework Statement

What is the remainder when (1*1!+2*2!+...+12*12!) Is divided by 13? Please give the answer along with the steps.

Homework Equations

The Attempt at a Solution

 

[ehild]

Homework Statement

What is the remainder when (1*1!+2*2!+...+12*12!) Is divided by 13? Please give the answer along with the steps.

Homework Equations

The Attempt at a Solution

We cannot give the answer. We give hints, to solve the problem by yourself.
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What does n! mean? Can you write the expression (1*1!+2*2!+...+12*12!) entirely with factorials?
Note that (k+1)! = (k+1)k!, determine (k+1)! - k!.