$$\sum^\infty_{n=0}\frac{(-1)^{n+1}}{(2n+1)!}$$ is approximated using the partial sum $$\sum_{n=0}^3\frac{(-1)^{n+1}}{(2n+1)!}$$
The error bound is $$\frac{(-1)^5}{9!}\approx -0.000003$$
Why is this an overestimation and not an underestimation since it is negative?
The true value is between the partial sum and the partial sum plus the error bound. So, if the error is negative, the partial sum is an overestimate.