Question $2$: $20$ Marks

PLEASE USE GNU OCTAVE $($GUI$)$

Evaluate the series ${\displaystyle \underset{n=1}{\overset{}{}}}{u}_n$ in which $u_n$ is unkown explicitly but is given in terms of a recurrence relation. The stopping condition on the summation is when given the following recurrence relation, $u_{n+1}=u_{n-1}^2+u_n^{1\mathrm{.}5},$ with $u_1=0\mathrm{.}2$ and $u_2=0\mathrm{.}5.$