Question

complex infinite series
is this right?

Answer 1

\[\sum_{ }^{ } \frac{ 1 + i }{ n^{2} }\]

Answer 2

then absolute convergence test gives \[\sum_{ }^{ } \ \left| \frac{ 1 + i }{ n^{2} } \right| = \sum_{ }^{ } \frac{ \sqrt{2} }{ n ^{2} }\]

Answer 3

\[\sqrt{2} * \sum_{ }^{ } \frac{ 1 }{ n ^{2} }\]

Answer 4

p test
p = 2 > 1 so convergent ??