Tính nhanh:\(\frac{4,8x0,5+16x0,25+20:10}{1000x0,06}\)
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(135,4 - 84,3) :2,5 - 10,46
= 51,1 :2,5 - 10,46
= 20,44 - 10,46 = 9,98
Tương tự nha
\(=10.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{10.11}\right)\)
\(=10.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+..+\frac{1}{10}-\frac{1}{11}\right)\)
\(=10\left(\frac{1}{2}-\frac{1}{11}\right)=10\cdot\frac{9}{22}=\frac{45}{11}\)
Bài 1:
\(A=\frac{3333}{101}\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)=\frac{3333}{101}\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\)
\(A=\frac{3333}{101}\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)
\(A=\frac{3333}{101}\left(\frac{1}{3}-\frac{1}{7}\right)=\frac{3333}{101}.\frac{4}{21}=\frac{1111.4}{101.7}=\frac{4444}{707}\)
Bài 2
\(A=\frac{2^{10}+1}{2^{10}-1}=\frac{2^{10}-1+2}{2^{10}-1}=1+\frac{2}{2^{10}-1}\)
\(B=\frac{2^{10}-1}{2^{10}-3}=\frac{2^{10}-3+4}{2^{10}-3}=1+\frac{4}{2^{10}-3}\)
Ta thấy \(2^{10}-1>2^{10}-3\Rightarrow\frac{2}{2^{10}-1}< \frac{2}{2^{10}-3}< \frac{4}{2^{10}-3}\)
Từ đó \(\Rightarrow1+\frac{2}{2^{10}-1}< 1+\frac{4}{2^{10}-3}\Rightarrow A< B\)
Bài 3\(P=\frac{\left(\frac{2}{3}-\frac{1}{4}\right)+\frac{5}{11}}{\frac{5}{12}+\left(1-\frac{7}{11}\right)}=\frac{\frac{5}{12}+\frac{5}{11}}{\frac{5}{12}+\frac{4}{11}}=\frac{\frac{55+60}{11.12}}{\frac{55+48}{12.11}}=\frac{115}{103}\)
=\(=\frac{1}{5}+\frac{1}{2.5}+\frac{1}{4.5}+\frac{1}{4.8}+\frac{1}{8.5.2}+\frac{1}{8.5.4}\)
\(=\frac{1+1+1+1+1+1}{5+2.5+4.5+4.8+8.5.2+8.5}\)
\(=\frac{6}{5.8}\)
\(=\frac{6}{40}\)
mk trả lời nhanh nhất tích đúng cho mk nhé
\(\frac{1}{5}+\frac{1}{10}+\frac{1}{20}+\frac{1}{40}+...+\frac{1}{1280}\)
\(=\left(\frac{1}{5}+\frac{1}{10}+\frac{1}{20}+\frac{1}{40}+...+\frac{1}{1280}\right)\cdot5\cdot\frac{1}{5}\)
\(=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}\right)\cdot\frac{1}{5}\)
\(=\left(1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...-\frac{1}{256}\right)\cdot\frac{1}{5}\)
\(=\left(1+1-\frac{1}{256}\right)\cdot\frac{1}{5}\)
\(=\left(2-\frac{1}{256}\right)\cdot\frac{1}{5}\)
\(=\frac{511}{256}\cdot\frac{1}{5}\)
\(=\frac{511}{1280}\)