The product of the first three terms in a positive geometric sequence is 1728. If the third term is decreased by 2, the three numbers will form an arithmetic sequence. Find the first three terms of the geometric sequence. Find the nth term of the geometric sequence in terms of n. Find the sum of the first n terms of the geometric sequence in terms of n. Find the sum to infinity of the geometric sequence, if it is convergent. Verify that 2n + 1/n2 (n + 1)2 = 1/n2 - 1/(n + 2)for all positive integer n. Using the identity in (i), find the exact value of Find the exact value of the infinite sum Let f (x ) = x - 5/(x + 1)(3x + 2) Convert f (x ) into the partial fraction form. Write  (x) as a series expansion up to and including the term in x3. State the range of values of x for which the expansion in (ii) is valid. Prove by mathematical induction that for any positive integer n, Prove by mathematical induction that for any integer n 5, 2n > n2.
