\(\left(1-\dfrac{1}{4}\right)\times\left(1-\dfrac{1}{9}\right)\times...\times\left(1-\dfrac{1}{576}\right)\times\left(1-\dfrac{1}{625}\right)\)
\(=\dfrac{3}{4}\times\dfrac{8}{9}\times\dfrac{15}{16}\times...\times\dfrac{575}{576}\times\dfrac{624}{625}\)
\(=\left(\dfrac{3}{2}\times2\right)\times\left(\dfrac{8}{3}\times3\right)\times\left(\dfrac{15}{4}\times4\right)...\times\left(\dfrac{575}{24}\times24\right)\times\left(\dfrac{624}{25}\times25\right)\)
\(=\dfrac{1\times3\times2\times4\times3\times5\times...\times23\times25\times24\times26}{2\times3\times4\times...\times25\times2\times3\times4\times...\times25}\)
\(=\dfrac{1\times2\times3\times4\times...\times24\times3\times4\times...\times26}{2\times3\times4\times...\times25\times2\times3\times4\times...\times25}\)
\(=\dfrac{1\times26}{2\times25}=\dfrac{26}{50}=\dfrac{13}{25}=0,52\)
=(1-1/2)(1-1/3)*...*(1-1/25)(1+1/2)(1+1/3)*...*(1+1/25)
=1/2*2/3*...*24/25*3/2*4/3*...*26/25
=1/25*26/2
=26/50=13/25
