Answer Happy

Don't copy other solutions
Compute the following Residue
2nki Zn +1 (b) Res zn-1 ten where ne N and k € {0, 1, ..., n – 1} (c) Res (z” sin-; 0), where neN (d) Res (2n(1-2); 0), where neN ) 0 zņ n Hint: In (d), the result from Q21 of Problem Set 3 may be useful 21. It is well-known that on D(0; 1), the geometric series Ek o zk converges to the holomorphic =0 function 1 - 1-z Now show that on D(0; 1) we have +00 k + 1 (1 – z)n+1 Σ(***). : zk n k=0 for each non-negative integer n.