challenge for programmable calculators

[Thomas Klemm]

Or just have a look at the roots: {0.04974, 0.857089, 1.50476, 15.5884}
Since \(f(1)=1\) it's obvious that \(f(n)<0\) for n in {2,...,15}.
To show this for n = 15 with your method isn't possible.
In this case we're lucky that we don't have to do that.