Question

S= (1+1/4).(1+1/9).(1+1/16).(1+1/25). ... .(1+1/121).(1+1/144)

 

Answer 1

Sửa đề : \(S=\left(1-\frac{1}{4}\right).\left(1-\frac{1}{9}\right).\left(1-\frac{1}{16}\right).....\left(1-\frac{1}{144}\right)\)

\(\Rightarrow S=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{143}{144}\) 

\(\Rightarrow S=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{11.13}{12.12}\) 

\(\Rightarrow S=\frac{1.2.3.....11}{2.3.4.....12}.\frac{3.4.5.....13}{2.3.4.....12}\)  

\(\Rightarrow S=\frac{1}{12}.\frac{13}{2}\) 

\(\Rightarrow S=\frac{13}{24}\)