cmi-entrance 2012 QB5

cmi-entrance · India · pgmath 10 marks Sequences and series, recurrence and convergence Series convergence and power series analysis
Show that a power series $\sum _ { n \geq 0 } a _ { n } z ^ { n }$ where $a _ { n } \rightarrow 0$ as $n \rightarrow \infty$ cannot have a pole on the unit circle. Is the statement true with the hypothesis that $\left( a _ { n } \right)$ is a bounded sequence? 
Show that a power series $\sum _ { n \geq 0 } a _ { n } z ^ { n }$ where $a _ { n } \rightarrow 0$ as $n \rightarrow \infty$ cannot have a pole on the unit circle. Is the statement true with the hypothesis that $\left( a _ { n } \right)$ is a bounded sequence?
Paper Questions
QA1 QA10 QA11 QA12 QA13 QA14 QA15 QA2 QA3 QA4 QA5 QA6 QA7 QA8 QA9 QB1 QB10 QB2 QB3 QB4 QB5 QB6 QB7 QB8 QB9