1. Simplify the following expression:

2. (a) Write the middle term of the expansion of by the binomial theorem.

2. (b) Find the value of if

and

2. (b) and reduce the result to a form having only positive exponents.

3. Find correct to three significant figures the negative root of the equation

4. Prove the rule for finding the sum of n terms of a geometrical progression of which the first term is a and the constant ratio is r.

4. Find the sum of 8 terms of the progression

5. A goldsmith has two alloys of gold, the first being pure gold, the second pure gold. How much of each must he take to produce 100 ounces of an alloy which shall be pure gold?