There is no elementary way to solve that. What we can do is let u= n+ 1 so the function can be written . We can further let v= -u so that . Now, the best way to solve such aninequality is to first solve the associateequation- here, which is, of course, the same as . And the solution to that is x= W(-0.01) where W is the "Lambert W function" (also known as the "omega function" or "product log" function) which isdefinedas the inverse function to . Looking at a graph of we can see there are two roots for , one at about -0.01 and the other at about -6.47. The inequality is satisfied for x below the root around -6 and above the root around -.01. (I used the "Newton-Raphson" iteration method to solve for those two values.)