1. Find an example of a sequence of real numbers satisfying each set of properties.(a) Cauchy, but not monotone(b) Monotone, but not Cauchy(c) Bounded, but not Cauchy2. Let (an) and (bn) be monotone sequences. Prove or give a counterexample.(a) The sequence (cn) given by cn = an + bn is monotone.(b) The sequence (cn) given by cn = an ⋅ bn is monotone

1. Find an example of a sequence of real numbers satisfying each set of properties. (a) Cauchy, but not monotone (b) Monotone, but not Cauchy (c) Bounded, but not Cauchy 2. Let (a n ) and (b n ) be...

1. Find an example of a sequence of real numbers satisfying each set of properties.

(a) Cauchy, but not monotone

(b) Monotone, but not Cauchy

2. Let (a_n) and (b_n) be monotone sequences. Prove or give a counterexample.

(a) The sequence (c_n) given by c_n
= a_n
+ b_n
is monotone.

(b) The sequence (c_n) given by c_n
= a_n
⋅ b_n
is monotone

May 05, 2022