Question

Let (an) and (bn) be two non negative sequences. Let cn=max{an,bn} for each n∈N.

Prove the following statements or give a counter example when false.

(a) If (an) and (bn) converge, so does (cn).

(b)If (an)and(bn) diverge, so does(cn)

Answer 1

both them are true since cn = max {an, bn}

Answer 2

i think i agree

Answer 3

@dumbcow you scared me, hehehe...

Answer 4

say a(n) converges to L
b(n) converges to M
then c(n) will converge to the greater of L or M

Answer 5

That all I have to say?

Answer 6

to me, I will add more like
if an>bn , then cn = an and an converges to L \(\rightarrow\) cn converges to L
if an <bn, then cn = bn and bn converges to M \(\rightarrow\) cn converges to M

Answer 7

And does the same go for divergence ?

Answer 8

yes, since c(n) is either a(n) or b(n) , then it will also diverge if both a(n),b(n) diverge

Answer 9

Ok and that's all I really have to say? There are no other theorems or proofs I have to show?

Answer 10

there may be, sorry im not sure not an expert with proofs
depends on the level of the class how thorough the proof needs to be

Answer 11

That's ok thank you.. there is a c and d part to this question..think if I close this one and post the rest of this quest u could take a look at that one too?

Answer 12

ok