z2n+1 7. Prove that sin z = (−1)”. converges absolutely for all z € C. Use (2n + 1)! n=0 this fact and Proposition 7 from the Week 5 Lecture Notes to conclude that ∞ z2n Σ(-1). also converges absolutely for all z E C. (2n)! COS 2 = n=0

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