# Given 2 series' an bn, what can be said about cn when

1. Apr 10, 2009

### Dell

given 2 unknown number series {an}$$^{infinity}_{n=1}$$ and {bn}$$^{infinity}_{n=1}$$, if it is know that {an}$$^{infinity}_{n=1}$$=infinity and {bn}$$^{infinity}_{n=1}$$=K,
K=constant unknown

{an+bn}$$^{infinity}_{n=1}$$
{an*bn}$$^{infinity}_{n=1}$$

i think that
{an+bn}$$^{infinity}_{n=1}$$= infinity, since:
{an+bn}$$^{infinity}_{n=1}$$={an}$$^{infinity}_{n=1}$$+{bn}$$^{infinity}_{n=1}$$= infinity + K = infinity

as for {an*bn}$$^{infinity}_{n=1}$$, i dont think anything can be said for sure, since K could be a number or 0,

am i right?? is there a proper mathematical way to write this?

2. Apr 10, 2009

### MathematicalPhysicist

Partially right.
If K=0 it's usually undefined, but if K>0 then K*infinity=infinity and if K<0 then... what can you say it equals to?

If you need to check the definitions there they are:
1. a_n=infinity iff for every M>0 there exists N such that for every n>N a_n>M
2. a_n=-infinity iff for every M<0 there exists N such that for every n>N a_n<M.

3. Apr 10, 2009

### Dell

i am asked is Cn converges when
Cn=An+Bn,---> does not converge

Cn=AnBn--->if |Bn|>0 - does not converge
but if Bn=0, then it is undefined, so what does that mean, diverge/converge/something else??

4. Apr 10, 2009

### MathematicalPhysicist

Well, now when I think of it if Bn=0, and An->infinity then AnBn->0 because AnBn=0 for every natural n.
If the question were, Bn->0 but not indetically 0, then it's undefined.