Answer
It is impossible to find $N$ such that the partial sum $S_N\gt 25$.
Work Step by Step
The series $$ \Sigma_{n=1}^\infty \frac{1}{n^n}$$
is a geometric series with the sum
$$\frac{1/2}{1-1/2}=1$$
So it is impossible to find $N$ such that the partial sum $S_N\gt 25$.
