The SQUEEZE Theorem for Sequences states that, " Suppose there are three rea number sequences, {r}, {yn} and {zn} such that {rn} → L, {zn} – L, ther {yn} → L." Read and study the proof of SQUEEZE THEOREM for real number sequences an use this theorem to prove that If sin n Vn E N, then if {--} ^ (: -}. then sin +0.

Let a ∈ G be such that |a| = ∞ . For m≠n prove that a^m ≠a^n

Let n > 3 and 2 (;) ')<(3) k n – k + + in two ways: (a) algebraic proof, and (b) combinatorial proof Hint for (b): show that the left side counts only some of the things counted by the right side.

Let f and g be any permutations. Show that the order of h=fgf^(-1) is the same as the order of g.