What is the answer to ((n+1)!)/((n+3)!)=600 ?

The answer to ((n+1)!)/((n+3)!)=600 is n=(-150+sqrt(906))/(60),n=-(150+sqrt(906))/(60)

Solve for n: ((n+1)!)/((n+3)!)=600

The solution is n=(-150+sqrt(906))/(60),n=-(150+sqrt(906))/(60)

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\frac{( n + 1 ) !}{( n + 3 ) !} = 600

n = \frac{- 150 + 906}{60}, n = - \frac{150 + 906}{60}

Decimal Notation

n = - 1.99833 \dots, n = - 3.00166 \dots

Solution steps

\frac{( n + 1 ) !}{( n + 3 ) !} = 600

Simplify

\frac{( n + 1 ) !}{( n + 3 ) !} : \frac{1}{( n + 3 ) ( n + 2 )}

\frac{1}{( n + 3 ) ( n + 2 )} = 600

Multiply both sides by

(n + 3) (n + 2)

1 = 600 (n + 3) (n + 2)

Solve

1 = 600 (n + 3) (n + 2) : n = \frac{- 150 + 906}{60}, n = - \frac{150 + 906}{60}

n = \frac{- 150 + 906}{60}, n = - \frac{150 + 906}{60}

\frac{( - 2 ) + x}{7 x} = 21

\frac{3 y + 4}{2 - 6 y} = \frac{- 2}{5}

\frac{1}{x ^{2}} + \frac{1}{( x - 2 ) ^{2}} = 2

\frac{x ^{2} + x ^{2} + 2 x + 1}{x ^{2} + x} = \frac{34}{15}

\frac{2}{3 \cdot ( x + 4 ) ^{2} - 8} = \frac{( 5 x )}{6}

What is the answer to ((n+1)!)/((n+3)!)=600 ?
The answer to ((n+1)!)/((n+3)!)=600 is n=(-150+sqrt(906))/(60),n=-(150+sqrt(906))/(60)
Solve for n: ((n+1)!)/((n+3)!)=600
The solution is n=(-150+sqrt(906))/(60),n=-(150+sqrt(906))/(60)