"ପ୍ରମାଣ ଯେ π ଗୋଟିଏ ଅପରିମେୟ ସଂଖ୍ୟା" ପୃଷ୍ଠାର ସଂସ୍କରଣ‌ଗୁଡ଼ିକ ମଧ୍ୟରେ ତଫାତ

:<math>\begin{align}N&=q^{\left\lfloor\frac n2\right\rfloor}A_n\left(\frac\pi2\right)\\&=q^{\left\lfloor\frac n2\right\rfloor}\frac{\left(\frac pq\right)^{n+\frac 12}}{2^nn!}\int_0^1(1-z^2)\cos\left(\frac\pi2z\right)\,dz.\end{align}</math>

 

 

:<math>\lim_{n\in\mathbb{N}}q^{\left\lfloor\frac n2\right\rfloor}\frac{\left(\frac pq\right)^{n+\frac 12}}{2^nn!}=0.</math>

 

ତେଣୁ ଯଦି ''n'' ବଡ଼, ''N''&nbsp;<&nbsp;1. ଅସଙ୍ଗତି!!

 

== References ==