Determine the generating function for the following sequence: (),-), (2),,(-1)" (a),.. where a is a real number.

Show that the sequence {1, -1, 1, -1, 1, -1, ..., (-1)n+1, ...} diverges.

Consider the following sequence where f(1)=2 2,-10,-22,-34,-46… What is the common difference? Enter the next three number. Define a recursive function f(n) for the sequence in terms of f(n-1) Define an explicit function f(n) for the sequence in terms of n.

Define a sequence sn by {S0, S₁, S2, ...} = {0, 1/1, 2, 1/3, 4, 1/5, ...}. Give a two- case definition for Sn.