\(A=\dfrac{1}{4}+\dfrac{1}{16}+...+\dfrac{1}{576}\)

=1/2^2(1+1/2^2+...+1/12^2)

1/2^2+1/3^2+...+1/12^2<1-1/2+1/2-1/3+...+1/11-1/12=11/12

=>1+1/2^2+1/3^2+...+1/12^2<1+11/12=23/12

=>A<23/12*1/4=23/48<23/46=1/2

Ta có :

 \(A=\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+...+\frac{1}{81}+\frac{1}{100}\)

\(=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{9^2}+\frac{1}{10^2}\)

\(\Rightarrow A>\frac{1}{2^2}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}+\frac{1}{10.11}\)

\(\Rightarrow A>\frac{1}{4}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)

\(\Rightarrow A>\frac{1}{4}+\frac{1}{3}-\frac{1}{11}\)

\(\Rightarrow A>\frac{65}{132}\left(đpcm\right)\)

Chúc bạn học tốt !!!! 

\(\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{9}\right)x\left(1-\frac{1}{16}\right)x...x\left(1-\frac{1}{576}\right)x\left(1-\frac{1}{625}\right)\)

\(=\frac{3}{4}x\frac{8}{9}x\frac{15}{16}x...x\frac{575}{576}x\frac{624}{625}=\frac{1x3}{1x4}x\frac{2x4}{3x3}x\frac{3x5}{4x4}x...x\frac{23x25}{24x24}x\frac{24x26}{25x25}\)

\(=\left(\frac{1}{1}x\frac{2}{3}x\frac{3}{4}x\frac{4}{5}x...x\frac{23}{24}x\frac{24}{25}=\frac{1x2x3x4x...x23x24}{1x3x4x5x...x24x25}=\frac{2}{25}\right)\left(\frac{3}{5}x\frac{4}{3}x\frac{5}{4}x\frac{6}{5}x...x\frac{25}{24}x\frac{26}{25}=\frac{3x4x5x6x...x25x26}{5x3x4x5x...x24x25}=\frac{26}{5}\right)\)

\(\frac{2}{25}x\frac{26}{5}=\frac{52}{50}=\frac{26}{25}\)

nguyễn như đạt sai rồi kết quả phải là 13/25 mk làm rùi 

ket qua =13/25 do dat a

0,52 nhé

tk cho mk nha

THAM KHẢO NHA 

https://olm.vn/hoi-dap/detail/56559485893.html

Đây là toán lớp 5 hay lớp 6 vậy.

Nếu đây là toán 6 thì tớ giải cho.