1000 : (x + \(\frac{1}{2}\) ) . 5 = 5 : \(4\frac{2}{3}\)
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\(\frac{2}{3}+\frac{1}{3}=\frac{6+3}{3}=\frac{9}{3}=3\)
\(\frac{3}{4}+\frac{2}{4}+\frac{1}{4}=\left(\frac{3}{4}+\frac{1}{4}\right)+\frac{1}{2}=1+\frac{1}{2}=1\frac{1}{2}=\frac{3}{2}\)
\(\frac{4}{5}+\frac{3}{5}+\frac{2}{5}+\frac{1}{5}=\left(\frac{4}{5}+\frac{1}{5}\right)+\left(\frac{3}{5}+\frac{2}{5}\right)=2+2=4\)
\(\frac{5}{6}+\frac{4}{6}+\frac{3}{6}+\frac{2}{6}+\frac{1}{6}=\left(\frac{5}{6}+\frac{1}{6}\right)+\left(\frac{4}{6}+\frac{2}{6}\right)+\frac{1}{2}=1+1\)\(+\frac{1}{2}=2\frac{1}{2}=\frac{5}{2}\)
ngu LÊ MĨ LINH
theo thứ tự :1,6/4 =1 và 1/2,2,5/2,500
\(\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times...\times\frac{1000}{999}\)
\(=\frac{3\times4\times5\times...\times1000}{2\times3\times4\times...\times999}=\frac{1000}{2}=500\)
\(1000-\left(x-\frac{1}{2}\right):5=5:4\frac{2}{3}\)
\(1000-5:\frac{14}{3}=\left(x-\frac{1}{2}\right):5\)
\(\frac{13985}{14}=\left(x-\frac{1}{2}\right):5\)
\(x-\frac{1}{2}=\frac{69925}{14}\)
\(x=\frac{34966}{7}\)
\(1000-\left(x-\frac{1}{2}\right):5=5:4\frac{2}{3}\)
\(1000-\left(x-\frac{1}{2}\right):5=\frac{15}{14}\)
\(\left(x-\frac{1}{2}\right):5=1000-\frac{15}{14}\)
\(\left(x-\frac{1}{2}\right):5=\frac{13985}{14}\)
\(\left(x-\frac{1}{2}\right)=\frac{13985}{14}\cdot5\)
\(x-\frac{1}{2}=\frac{69925}{14}\)
\(x=\frac{69925}{14}+\frac{1}{2}\)
\(x=\frac{34966}{7}\)
Tính
a)
\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{9999}{10000}\\ =\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}....\frac{99.101}{100}\\ \)
\(=\left(\frac{1.2.3...99}{2.3...100}\right).\left(\frac{3.4.5...101}{2.3.4...100}\right)\\ =\frac{1}{100}.\frac{101}{2}=\frac{101}{200}\)
b)
\(\frac{1}{2^2}+\frac{1}{3^2}+....+\frac{1}{n^2}\\ < \frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{\left(n-1\right)n}\\ \)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{n-1}-\frac{1}{n}\\ =1-\frac{1}{n}< 1\)
\(1000:\left(x=\frac{1}{2}\right).5=5:4\frac{2}{3}\)
\(=1000:\left(x+\frac{1}{2}\right).5=\frac{15}{14}\)
\(=>\left(x+\frac{1}{2}\right).5=\frac{2800}{3}\)
\(=>x+\frac{1}{2}=\frac{560}{3}\)
\(=>x=\frac{1117}{6}\)
Ủng hộ nha