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

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

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

simplify

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

(n + 1)^{2}

Solution steps

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

Apply exponent rule:

a^{2} = aa

(n + 1)!^{2} = (n + 1)! (n + 1)!

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

Apply exponent rule:

a^{2} = aa

n!^{2} = n! n!

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

Cancel the factorials:

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

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

= (n + 1) (n + 1)

Apply exponent rule:

aa = a^{2}

(n + 1) (n + 1) = (n + 1)^{2}

= (n + 1)^{2}

2 x^{2} + 3 x = 42 - 2 x

2 x^{3} - 3 x^{2} - 2 x + 3

2 x^{2} - 3 x = 2 x - 2

v^{2} - 5 v + 4

(t - 4)^{2} = (t + 4)^{2} + 16

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