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Leibniz Series for π
Summary In this article we prove the Leibniz series for π which states that <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block"> <m:mfrac> <m:mi>π</m:mi> <m:mn>4</m:mn> </m:mfrac> <m:mo>=</m:mo> <m:mstyle displaystyle="true"> <m:munderover> <m:mo>∑</m:mo> <m:mrow> <m:mi>n</m:mi> <m:mo>=</m:mo> <m:mn>0</m:mn> </m:mrow> <m:mi>∞</m:mi> </m:munderover> <m:mrow> <m:mfrac> <m:mrow> <m:msup> <m:mrow> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mo>−</m:mo> <m:mn>1</m:mn> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mrow> <m:mi>n</m:mi> </m:msup> </m:mrow> …