Consider two series sum_(n=1)^oo 1/2pinZ and sum_(n=0)^oo 1/pi^2n. Which o

Amari Flowers

Amari Flowers

Answered question


Consider two series n=112πnZandn=01π2n. Which of them converges?

Answer & Explanation



Skilled2021-08-14Added 102 answers

Series A: n=112πn=12π{11+12+13+}
Harmonic series – Divergent
Series B: n=01π2n={(1π2)+(1π2)2+}
Geometric series, so 1π2<1 – Convergent
Thus, only series B converges.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?