Need help in this Factorial question

The question states this:

If

(n+1)! + n^2(n-1)! = (an+1)n!

find the value of a

I got upto a point where i simplified the expression to:

(n-1)! (2n^2 + n)

bump

is it possible to factorise your expression further?

is it possible to factorise your expression further?

I dont know. Would (n-1)! be the same after being taken out as a common factor, or would it be just be (n-1).

I meant a common factor in the second bracket.

Original post by brownguytorule

The question states this:

If

(n+1)! + n^2(n-1)! = (an+1)n!

find the value of a

I got upto a point where i simplified the expression to:

(n-1)! (2n^2 + n)

Try expanding the second bracket, thinking carefully about how you write a factorial in long form, namely:

n! = n \cdot (n-1) \cdot (n-2)...

... and

(n-1)! = (n-1) \cdot (n-2) \cdot (n-3)...

So what do you get when you multiply the factorial of

n-1

n

, and then

2n^2

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