Real Analysis Answers

Give an upper bound and a lower bound for the expression 1/(a^(4)+3a^(2)+1) if a∈R

Let (X d) be metric space and X is unbounded then d_(1) defined as d_(1)=(d(x y))/(1+d(x y)) x y in X is

a)metric and unbounded

b)metric but may be bounded or unbounded c)metric and bounded

Show that x inverse is not equal to 0 and is unique

Prove A∩(B∩C)=(A∩B)∩C

show that the series 1 - 1/2³ + 1/3³ - 1/4³ + 1/5³ - .... is absolutely convergent

if a sequence ⟨Sn⟩ is defined by Sn = Sn/1-Sn-1, s>0, s1>0. then show that the sequence converges to the positive root of the equation x²+x-5=0