Question

Tinh nhanh:

\(\frac{6}{2.5}+\frac{6}{5.8}+\frac{6}{8.11}+......+\frac{6}{299.302};\)

So sanh cac phan so sau ma khong can thuc hien cac phep tinh o mau

\(A=\frac{54.107-53}{53.107+54}\)                   \(B=\frac{135.269-133}{134.269+135}\)

Answer 1

\(\frac{6}{2.5}+\frac{6}{5.8}+\frac{6}{8.11}+...+\frac{6}{299.302}\)

\(=2\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+..+\frac{3}{299.302}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{299}-\frac{1}{302}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{302}\right)=2.\frac{75}{151}=\frac{150}{151}\)

\(A=\frac{54.107-53}{53.107+54}=\frac{\left(53+1\right).107-53}{53.107+54}\)

\(=\frac{53.107+107-53}{53.107+54}=\frac{53.107+54}{53.107+54}=1\)

\(B=\frac{135.269-133}{134.269+135}=\frac{\left(134+1\right)269-133}{134.269+135}\)

\(=\frac{134.269+269-133}{134.269+135}=\frac{134.269+136}{134.269+135}>1\)

\(\Rightarrow B>A\)