Question

Rewrite 4n^2+2n as a factorial.

Answer 1

4n²+2n as a factorial is given as:

`= (2n+1)!/(2n-1)!`

Explanation:

We are given an expression which has to be converted into factorial form.

The expression is as follows:

`4n^(2) + 2n\\ = 2n(2n+1)\\ = (2n+1)2n\\`

Now we know that 2n+1 and 2n differs by '1' and the next smaller term is '2n-1'.

Hence, multiplying and dividing by '(2n-1)!'; we get:

`= ((2n+1)(2n)(2n-1)!)/(2n-1)!`

we know that x(x-1)(x-2)! = x!, so:

`= (2n+1)!/(2n-1)!`