for i = 1,2, 3. Suppose also that P(X = i) = for i = 4, x. 1,2, 3. 8. Suppose P(X,n = i) = 3n+6 Prove that the sequence X, →

For the recursively defined function T(n)= ST(1/2) + 3 Which of the following best reflects the two statements: A) T (n) =_-_ (nlgn) B) T(n) = O(2.25) A. Only A is TRUE B. Only B is TRUE C. Both A and B are TRUE D. Both A and B are FALSE

Let b1, b2, b3,... be the sequence of numbers defined by b1 = 1, and b, V6 + bn-1 if n > 2. Prove that 0 1.

2. Find the converse and the contrapositive of the following statemnents: (a) If m divides 2+j², then m divides i and n divides j (Here, m, i and j are fired numbers.) (b) If f(r) = S(y), then r = (Here the numbers r, y and the function f are fired.) (c) If the sequence (a,) of real mumbers is convergent, then it's bounded. (Here (a,) is fized, ) (d) The set A is a subset of the set B if any element a in A is an element of B.(Here, A and B are fized.)

Suppose that the sequence x0, x₁, x2... is defined by x0 = 0, x₁ = 7, and xk+2 = xk for k≥0. Find a general formula for xk. Be sure to include parentheses where necessary, e.g. to distinguish 1/(2k) from 1/2k. xk = 0