How does one solve the following inequality for n, without trial and error, and assuming n can only be an integer?
The inequality is $(n+1)!-1>10^9$.
I want to find the minimum value of n such that $(n+1)!-1>10^9$. How does one do this without graphing the inequality, or using a calculator? I figured it out throwing trial and error on a calculator, but I desire a more elegant solution, one that gets to the answer algebraically, and without a calculator or graph. Any suggestions?