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Unformatted text preview: ³ X k b k ³ ³ is bounded for all n ∈ N . 5. Investigate the convergence of ∞ X k =1 z k k ! . 6. Find the domain of convergence of the series ∞ X k =1 z k k . 7. Expand the function f ( z ) = 1+2 z z 2 + z 3 into a series involving powers of z . 8. Prove that ∞ X k =1 ´ √ n + 1-√ n µ diverges. Observe that this is a divergent series with general term tending to . You can show it. Notes 1 Please visit: http://www.math.boun.edu.tr/deptcourses/math232...
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This note was uploaded on 11/08/2011 for the course MATH 232 taught by Professor Gurel during the Spring '11 term at Boğaziçi University.
- Spring '11