1) Prove or disprove the following: a) limit n--infinity 1/n 2 =1 b) If A is a bounded, nonempty set, inf A sup A c) The function f:

1) Prove or disprove the following:

a) limit n-->infinity 1/n2=1

b) If A is a bounded, nonempty set, inf A ≤ sup A

c) The function f: R → R defined by f(x) = x4  is surjective

2) Use induction to prove the following:

∑ (2n-1)= n2

(the summation is from 1 to n)

Q1. lim n →∞ 1=0n2 Hence, it is not equal to 1 Q2.Proof by Contradiction Assume sup A is not contained in the closure of A. Sup A is then not a limit point of A. So there exists an open set...