If the first problem does indeed say that the length of the base is three times its width, then, taking w for the width, the length is 3w and, taking h for the height, the volume is given by and the total surface are is . You can solve the surface area equation for h in terms of w, replace h by that in the volume equation, to have an equation in w only. Differentiate with respect to w and set the derivative equal to 0.
If the second problem is really , to use induction, the first step is to show that it is true for the first case, n= 1.
Then the sum is just 1- 1= 0 while the right side is 1((1- 1)(1+ 2)/4= 0.
Now show that "if this is true for n= k, it is also true for n= k+1." That is, If then . Notice that .