Let (An) and (Bn) be monotone sequences. Prove or give a counter example
A) The sequence (Cn) given by Cn = KAn is monotone for any k element of R
B) The sequence (Cn) given by Cn = An/Bn is monotone.
Let (An) and (Bn) be monotone sequences. Prove or give a counter example
A) The sequence (Cn) given by Cn = KAn is monotone for any k element of R
B) The sequence (Cn) given by Cn = An/Bn is monotone.
a_n is either:
a_1<=a_2<=a_3<=...
Or,
a_1>=a_2>=a_3>=...
If k=0 nothing to proof. (Why?)
If k>0 then,
ka_1<=ka_2<=ka_3<=...
Or,
ka_1>=ka_2>=ka_3>=...
If k<0 then,
ka_1>=ka_2>=ka_3>=...
Or,
ka_1<=ka_2<=ka_3<=...