This morning I was interested in the following formula f(x)=(1+((-1)/3+(1/5+((-1)/7+(1/9+(-1/11+(1/13+((-1)/15+(1/17+((-1)/19+(1/21+((-1)/23+(1/25+(-1/27+(1/29+((-1)/31+(1/33+\cdots )/x^2)/x^2)/x^2)/x^2)/x^2)/x^2)/x^2)/x^2)/x^2)/x^2)/x^2)/x^2)/x^2)/x^2)/x^2)/x^2)/x ; I have deduced the following formulas. Pi/6=(1+((-1)/3+(1/5+((-1)/7+(1/9+(-1/11+(1/13+((-1)/15+(1/17+((-1)/19+(1/21+((-1)/23+(1/25+(-1/27+(1/29+((-1)/31+(1/33+\cdots )/3)/3)/3)/3)/3)/3)/3)/3)/3)/3)/3)/3)/3)/3)/3)/3)/sqrt(3); approximative value Pi/6=(1+((-1)/3+(1/5+((-1)/7+(1/9+(-1/11+(1/13+((-1)/15+(1/17+((-1)/19+(1/21+((-1)/23+(1/25+(-1/27+(1/29+((-1)/31+(1/33 )/3)/3)/3)/3)/3)/3)/3)/3)/3)/3)/3)/3)/3)/3)/3)/3)/sqrt(3); Pi/4=(1+((-3)^(-1)+(5^(-1)+((-7)^(-1)+(9^(-1)+(-(11)^(-1)+((13)^(-1)+((-15)^(-1)+((17)^(-1)+((-19)^(-1)+((21)^(-1)+((-23)^(-1)+((25)^(-1)+(-(27)^(-1)+((29)^(-1)+((-31)^(-1)+((33)^(-1)+\cdots )/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1; Pi/6=(1+(1/6+(3/40+(5/112+(35/1152+(63/2816+(231/13312+(143/10240+(6435/557056+(12155/1245184+\cdots )/4)/4)/4)/4)/4)/4)/4)/4)/4)/2; Pi/4=(1+(1/6+(3/40+(5/112+(35/1152+(63/2816+(231/13312+(143/10240+(6435/557056+(12155/1245184+ \cdots )/2)/2)/2)/2)/2)/2)/2)/2)/2)/sqrt(2); Pi/2=(1+(1/6+(3/40+(5/112+(35/1152+(63/2816+(231/13312+(143/10240+(6435/557056+(12155/1245184+\cdots )/1)/1)/1)/1)/1)/1)/1)/1)/1)/1; a_(n):(2n)!/(2^(2n)*(n!)^2*(2n+1)); Catalan number G=(1+(-(3)^(-2)+(5^(-2)+(-(7)^(-2)+(9^(-2)+(-(11)^(-2)+((13)^(-2)+(-(15)^(-2)+((17)^(-2)+(-(19)^(-2)+((21)^(-2)+(-(23)^(-2)+((25)^(-2)+(-(27)^(-2)+((29)^(-2)+(-(31)^(-2)+((33)^(-2)+?)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1; Zeta function zeta(m)=(1+(2^(-m)+(3^(-m)+(4^(-m)+(5^(-m)+(6^(-m)+(7^(-m)+(8^(-m)+(9^(-m)+(10^(-m)+(11^(-m)+(12^(-m)+(13^(-m)+(14^(-m)+(15^(-m)+(16^(-m)+(17^(-m)+\cdots )/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1)/1;