99 (3) Evaluate E (-3). (Hint: Since there are 100 terms in the sum, it isn't a good idea to write them all out and add. Use the formula for the sum of terms of a geometric sequence. Leave the answer with exponents rather than using a calculator to try to get a decimal approximation of the answer.) (4) (a) List the first four terms of the sequence defined recursively by ao = 2, and, for n 2 1, a-_1 - 1. an = 207- (b) List the first five terms of the sequence with initial terms uj = 1 and u2 = 5, and, for n 2 3, un = 5un-1 - 6un-2. Guess a closed form formula for the sequence. Hint: The terms are simple combinations of powers of 2 and powers of 3. (5) Give a recursive definition of the geometric sequence with initial term a and common ratio r. Hint: an = ar"-isn't a correct answer since this formula isn't recursive. Make sure you write down a recursive formula: (1) give the initial term, and (2) give the rule for building new terms from previous terms. (6) (bonus) Express in summation notation: I 3 5 2n - 1' the sum of the reciprocals of the first n odd positive integers. (Note that there are n terms in the sum.) Hint: A common mistake on this question is using the symbol n both as an index for summation and to indicate the last term to be added in. To make sure you haven't fallen into that trap, replace every n in your formula by a specific value, say 5. The result should 1 1 + 1 1 be a sum = + +