Find minimum value of Sum $\displaystyle\sum _{k=1}^n a_k^2$ for reals satisfying $\displaystyle\sum _{k=1}^n a_k=1$ .
This is first time I am encountering such problem . How to approach such problem where there are so many variables and a little information ? Most of time I use AM - GM inequalities and derivatives for maxima and minima but nothing seem to work here . This was some last year exam question and options are in terms of n .