What is ((2(n+1))!)/((2n)!) ?

The solution to ((2(n+1))!)/((2n)!) is (2n+2)(2n+1)

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simplify ((2(n+1))!)/((2n)!)

simplify

\frac{( 2 ( n + 1 ) ) !}{( 2 n ) !}

(2 n + 2) (2 n + 1)

Solution steps

\frac{( 2 ( n + 1 ) ) !}{( 2 n ) !}

Expand

2 (n + 1) : 2 n + 2

= \frac{( 2 n + 2 ) !}{( 2 n ) !}

Cancel the factorials:

\frac{n !}{( n - m ) !} = n \cdot (n - 1) \dots (n - m + 1), n > m

\frac{( 2 n + 2 ) !}{( 2 n ) !} = (2 n + 2) (2 n + 1)

= (2 n + 2) (2 n + 1)

(y^{3})^{2} y^{4}

x^{3} \times x^{4}

5 (3 x + 2) - 2 (4 x - 1)

12 x^{2} y^{2} - 6 x y^{3} + 3 x y^{2} z

What is ((2(n+1))!)/((2n)!) ?
The solution to ((2(n+1))!)/((2n)!) is (2n+2)(2n+1)