Can we assume that this is (e^(npi i)}/(1+ 3^n)?

Is so, that's east: |e^(npi i)|<= 1 while the denominator increases without limit.

sinh(z)= (e^(z)- e^(-z))/2i so sinh(npi i)/2= [(e^(n pi i)- e^(n pi i))/2] (1/2i)= sin(n pi) (-i/2) and sin(n pi)= 0 for all n.b) sinh[(npii)/2]

a) I presuming that the dominant term is e, but when I divide by it I get

1/[(1/e^npii)+(3^n)/e^npii]

Is this the right way of doing it? If not can someone point me in the right direction.

b)For this one I had

sinh[(npii)/2]=(e^(npii/2) - e^(-npii/2))

I tired a way using the the triangle inequality followed by the squeeze rule, but that came out wrong, so I dont know where I went wrong.

If anyone could please, please help, I would be very grateful.

Thanx

Bex