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\(a\times\frac{1}{2}=\frac{a}{2}\)
Vì số nào nhân với 1 cũng bằng chính số đó thôi
\(\left(x-\frac{2}{5}\right)×\frac{1}{2}=1=>\left(x-\frac{2}{5}\right)=1:\frac{1}{2}=>\left(x-\frac{2}{5}\right)=2=>x=2+\frac{2}{5}=>x=\frac{12}{5}\)
vậy \(x=\frac{12}{5}\)
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{132}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{11.12}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{11}-\frac{1}{12}\)
\(=\frac{1}{1}-\frac{1}{12}\)
\(=\frac{11}{12}\)
\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{132}\)
\(A=\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+...+\frac{1}{11x12}\)
\(A=\frac{2-1}{1x2}+\frac{3-2}{2x3}+\frac{4-3}{3x4}+\frac{5-4}{4x5}+...+\frac{12-11}{11x12}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{11}-\frac{1}{12}\)
\(A=1-\frac{1}{12}=\frac{11}{12}\)
25%.x+1/2.x=12
=> 1/4.x+1/2.x=12
=> x.(1/4+1/2)=12
=> x.0,75 =12
=> x =12:0,75
=> x =16
Vậy x=16
25/100.x + 1/2.x = 12
1/10.x + 1/2.x =12
(1/10 + 1/2 ).x =12
( 1/10 + 5/10 ).x =12
6/10 = 3/5.x = 12
x = 12 : 3/5
x = 12 . 5/3
x = 20
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\)
=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\)
=\(\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+\frac{6-5}{5.6}+\frac{7-6}{6.7}+\frac{8-7}{7.8}+\frac{9-8}{8.9}\)
=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)
=\(1-\frac{1}{9}=\frac{8}{9}\)
1/2 + 1/6 + 1/12 + ... + 1/72
= 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/8.9
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/8 - 1/9
= 1 - 1/9
= 8/9