Question $3$:

a$.)$ Use MATLAB to show that the sum of the infinite series

$)=(0,2,$dots,$m$ converges to $ln2.$ Do it by computing the sum for

i$.)m=10$

ii$.)m=500$

iii.$)m=10,000$

For each part create a vector $n,$ and then use element$-$by$-$element calculations to compute the series.

Question $4$:

A cone shaped container is designed to have a volume of $315m^3.$ Determine the radius, $r,$ of the base and the surface areas, $S,$ of the container with the heights, $h$ of $5,6,7,8,9,10$ and $12m.$

The volume, $V,$ and the surface area, $S,$ of the containers are given by:

$V=\frac{1}{3}{r}^{2}h$ and $S=r\sqrt[\phantom{2}]{r^2+h^2}$

The program should then display the output in tabular form in the following formats:

$\backslash$table$[[$Height$,$Radius,Surface Area$],[5,$X$.$xx$,$Xxx$.$xxx$],[6,$X$.$xx$,$Xxx$.$xxx$],[7,$X$.$xx$,$Xxx$.$xxx$],[8,$X$.$xx$,$xxx$.$xxx$],[..,.....,......]]$