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

Amari Flowers 2021-08-13 Answered
Consider two series n=112πnZandn=01π2n. Which of them converges?
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Expert Answer

pierretteA
Answered 2021-08-14 Author has 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.

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