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\(B=\frac{1}{2^2}.\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}\right)\)
\(\rightarrow\frac{A}{B}=\frac{\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}^2}{\frac{1}{4}\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}\right)}=\frac{1}{\frac{1}{4}}=4\)
\(B=\frac{1}{4^2}+\frac{1}{6^2}+\frac{1}{8^2}+....+\frac{1}{200^2}=\frac{1}{\left(2.2\right)^2}+\frac{1}{\left(2.3\right)^2}+\frac{1}{\left(2.4\right)^2}+...+\frac{1}{\left(2.100\right)^2}\)
\(B=\frac{1}{2^2.2^2}+\frac{1}{2^2.3^2}+\frac{1}{2^2.4^2}+...+\frac{1}{2^2.100^2}=\frac{1}{2^2}.\frac{1}{2^2}+\frac{1}{2^2}.\frac{1}{3^2}+\frac{1}{2^2}.\frac{1}{4^2}+...+\frac{1}{2^2}.\frac{1}{100^2}\)
\(B=\frac{1}{2^2}.\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+....+\frac{1}{100^2}\right)=\frac{1}{4}.A\)
\(\Rightarrow\frac{A}{B}=\frac{A}{\frac{1}{4}A}=\frac{A}{\frac{A}{4}}=A.\frac{4}{A}=4\)
xin loi may anh tai tui moi lop 6 thui ha
\(B=\frac{1}{4^2}+\frac{1}{6^2}+\frac{1}{8^2}+..+\frac{1}{100^2}=\frac{1}{\left(2.2\right)^2}+\frac{1}{\left(2.3\right)^2}+\frac{1}{\left(2.4\right)^2}+..+\frac{1}{\left(2.100\right)^2}\)
\(B=\frac{1}{2^2.2^2}+\frac{1}{2^2.3^2}+\frac{1}{2^2.4^2}+..+\frac{1}{2^2.100^2}=\frac{1}{2^2}.\frac{1}{2^2}+\frac{1}{2^2}.\frac{1}{3^2}+\frac{1}{2^2}.\frac{1}{4^2}+..+\frac{1}{2^2}.\frac{1}{100^2}\)
\(=\frac{1}{2^2}.\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}\right)=\frac{1}{4}.A\)
\(=>\frac{A}{B}=\frac{A}{\frac{A}{4}}=4\)
A/B=A/A/4=4
Biến đổi bt B=A/4 là đc
dạ em mới học lớp 6