3. and reduce the resulting expression to its simplest form.
4. State and prove the formula for the sum of the first n terms of a geometric progression in which a is the first term and r the constant ratio.
5. A state legislature is to elect a United States senator, a majority of all the votes cast being necessary for a choice. There are three candidates, A, B, and C, and 100 members vote. On the first ballot A has the largest number of votes, receiving 9 more votes than his nearest competitor, B; but he fails of the necessary majority. On the second ballot C's name is withdrawn, and all the members who voted for C now vote for B, whereupon B is elected by a majority of 2. How many votes were cast for each candidate on the first ballot?
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
ALGEBRA A
Time: One Hour and Three Quarters