# AGM Calculator

## Calculates the arithmetic-geometric mean (AGM).

 $Arithmetic-geometric\ mean\ AGM(a,b)\\[15]a_0=a,\ b_0=b\\\vspace{20}a_{n+1}={\large\frac{1}{2}}(a_n+b_n),\hspace{20}b_{n+1}=\sqrt{a_nb_n},\\\vspace{20}AGM(a,b)=\lim_{n\to\infty}a_n=\lim_{n\to\infty}b_n\\$

 a b [ maximum loop n ] 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 The calculation ends when two consecutive results are the same.The accuracy of AGM improves by increasing the number of digits for calculation. $\normal Arithmetic-geometric\ mean\ AGM(a,b)\\[10](1)\ a_0=a,\ b_0=b\\\vspace{20}(2)\ a_{n+1}={\large\frac{1}{2}}(a_n+b_n),\hspace{20}b_{n+1}=\sqrt{a_nb_n},\\\vspace{20}(3)\ a_1\ge a_2\ge a_3\ge ... \ge b_3\ge b_2\ge b_1\\\vspace{20}(4)\ AGM(a,b)=\lim_{n\to\infty}a_n=\lim_{n\to\infty}b_n\\$

AGM
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