Hey,

I'm just studying for my exam next week and I've found a few of these true or false problems I'm not 100% with,

For the first one, I would say its entire since both functions are entire, and also because the product of two entire functions is entire, so e^xcosy is entire.

So f(z) is entire, True.

Is that correct? I just get paranoid with these T/F questions because in some of them are tricky things you can miss and ruin the question.

For the second one I would think that the sequence would converge because the sum diverges if the sequence diverges, so the sum cant converge if the sequence diverges. So True.

For the third one, I not sure at all about the convergence of Laurent series, where would I start with this one?

And for the last, I believe its false because say if it was e^z/cosz then its not entire cause of the singularity at 0, but then i was thinking it would be entire so long as the function doesn't ever = 0 so I'm in a bit of a pickle. In the exam I would say false, because it doesn't specify any two entire functions.

Do you guys think what I have thought is ok?

Thanks in advanced