My book states that for large n and small a, $$\dfrac{1}{(n+a)^2} - \dfrac{1}{(n)^2} \approx -\dfrac{2a}{n^3}$$
Let $f(x) = \dfrac{1}{x^2}$, $$ df = -\dfrac{2}{n^3}dx$$ with $$dx = a$$ and so the above result follows. But the only restriction with using differentials is that a must be small. How do I say mathematically that n must be large for the approximation to be reasonable?
I have tried calculating with n = 0.01 and a = 0.5, I got an error of $10^6$. Gosh!