Question 1185279
<br>
Check the form of your equation and re-post.<br>
The equation as you show it has no solution in integers.<br>
If the equation you show is in fact correct, then....<br>
{{{(n+1)!=(11(n-1)/2)((n+3)!/3!)}}}
{{{(n+1)!=(11(n-1)(n+3)!)/12}}}
{{{12(n+1)!=11(n-1)(n+3)!}}}
{{{12=11(n-1)((n+3)!/(n+1)!)}}}
{{{12=11(n-1)(n+3)(n+2)}}}
{{{12 = 11(n-1)(n^2+5n+6)}}}
{{{12 = 11(n^3+4n^2+n-6)}}}
{{{12 = 11n^3+44n^2+11n-66}}}
{{{11n^3+44n^2+11n-78=0}}}<br>
Use a graphing calculator or some numerical method to find<br>
ANSWER: x=1.0864914 to 7 decimal places<br>