Convergent and Divergent problem

[danni7070]

If I have $$(a_n + b_n)^n = c_n$$ where a_n is convergent and b_n divergent. Is c_n then divergent?

And what if a_n and b_n were divergent, would c_n be divergent also?

but what if they were both convergent then surely c_n is convergent right?

I can't see a rule or a theorem that tells me this is correct and frankly it is getting on my nerve.

Somebody here who knows?

Thanks.

 

[sutupidmath]

Hve u tried an epsylon- delta proof? I think it might work.

 

[NateTG]

No conclusion is possible for the convergence of $c_n$.

$$a_n=b_n=0$$
$$a_n=b_n=1$$
$$a_n=0, b_n=(-1)^n \times \frac{1}{4}$$
$$a_n=1, b_n=(-1)^n$$
$$a_n=b_n=(-1)^n$$
$$a_n=b_n=(-1)^n \times \frac{1}{4}$$