If we have $N$ assets which are uncorrelated, but have the same mean return of $\mu$ but the variances are different where $\sigma_i^2$ is the variance of each asset $i = 1, 2,...,N$ how can you write a formula for the minimum-variance point? Write the result in terms of $\sigma_p^2=\sum_{i=1}^N{1/\sigma_i^2}$.
I tried solving the minimization problem by minimizing the portfolio variance subject to the weights summing to one, however when taking the inverse of the matrix to get the weights I cannot seem to write an elegant solution. Any help would be appreciated.