Evaluate a general solution and prove by mathematical induction:

General solution is 

Proof:
Let the equation be equal to some sum,

Now, we need to find a link between each unit.



Let's consider a pattern by taking the first four terms.






Now, let's consider their summations and we'll call them .






One aspect of the sequence should be jumping out now; the numerator is always one less than the denominator.

Now, let's consider a pattern with the denominator.
We know that 2! = 2, 3! = 6, 4! = 24, and 5! = 120
We also know that they are the denominators of the sequences.

So, we can generalise our equation as:



MI should be fairly simple now, if you have any problems, feel free to message me!

Ibelieve its 0 but i am not sure