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1/1+2+1/1+2+3+1/1+2+3+4+1/1+2+3+4+5
=1/3+1/6+1/10+1/15
lấy mẫu số chung là 30,ta có:
10/30+5/6+3/10+2/30
=20/30=2/3
(3/10+4/5x1/2):1/8/9-1/1/3
=(3/10+4/10):17/9-4/3
=7/10:17/9-4/3
=63/170-4/3
=-491/510
1)
a) \(x+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}=5\)
\(x+\frac{64}{128}+\frac{32}{128}+\frac{16}{128}+\frac{8}{128}+\frac{4}{128}+\frac{2}{128}+\frac{1}{128}=5\)
\(x+\frac{127}{128}=5\)
\(x=5-\frac{127}{128}=\frac{513}{128}\)
b) \(x+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}+\frac{1}{2187}=3\)
\(x+\frac{729}{2187}+\frac{243}{2187}+\frac{81}{2187}+\frac{27}{2187}+\frac{9}{2187}+\frac{3}{2187}+\frac{1}{2187}=3\)
\(x+\frac{2186}{2187}=3\)
\(x=3-\frac{2186}{2187}=\frac{4375}{2187}\)
2)
a) \(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(=1-\frac{1}{6}=\frac{5}{6}\)
b) \(5\frac{1}{2}+3\frac{5}{6}+\frac{2}{3}\)
\(=\left(5+3\right)+\left(\frac{1}{2}+\frac{2}{3}+\frac{5}{6}\right)\)
\(=8+\left(\frac{3}{6}+\frac{4}{6}+\frac{5}{6}\right)\)
\(=8+2=10\)
c) \(7\frac{7}{8}+1\frac{4}{6}+3\frac{3}{5}\)
\(=\left(7+1+3\right)+\left(\frac{7}{8}+\frac{2}{3}+\frac{3}{5}\right)\)
\(=11+\left(\frac{105}{120}+\frac{80}{120}+\frac{72}{120}\right)\)
\(=11+\frac{257}{120}=\frac{1577}{120}\)
3) Gọi số đó là x. Theo đề ta có :
\(\frac{16-x}{21+x}=\frac{5}{7}\)
\(7\left(16-x\right)=5\left(21+x\right)\)
\(112-7x=105+5x\)
\(112-105=7x-5x\)
\(7=2x\)
\(x=\frac{7}{2}=3,5\) ( vô lí )
Vậy không có số tự nhiên để thõa mãn điều kiện trên.
\(3\frac{4}{7}4\frac{2}{5}2\frac{1}{2}\)
\(=\frac{275}{7}\)
\(3\frac{1}{5}+\frac{3}{4}-\frac{1}{2}:\frac{2}{7}=\frac{16}{5}+\frac{3}{4}-\frac{7}{4}=\frac{11}{5}\)
\(3\frac{4}{7}4\frac{2}{5}2\frac{1}{2}=\frac{275}{7}\)
\(3\frac{1}{5}+\frac{3}{4}+\frac{1}{2}:\frac{2}{7}\)
\(=3\frac{1}{5}+\frac{3}{4}+\frac{7}{4}\)
\(=\frac{11}{5}\)
a,=25/6;7/6=25/6x6/7=25/7
b,=7/2x32/6=56/3
c,=17/5-11/10=34/10-11/10=23/10
d,=8/3+11/4=32/12+33/12=65/12
\(a.1\frac{1}{3}+2\frac{1}{2}\)
\(=\frac{4}{3}+\frac{5}{2}\)
\(=\frac{8}{6}+\frac{15}{6}\)
\(=\frac{23}{6}\)
\(b.3\frac{2}{5}-1\frac{1}{7}\)
\(=\frac{17}{5}-\frac{8}{7}\)
\(=\frac{119}{35}-\frac{40}{35}\)
\(=\frac{79}{35}\)
\(c.3\frac{1}{2}.1\frac{1}{7}\)
\(=\frac{7}{2}.\frac{8}{7}\)
\(=4\)
\(d.4\frac{1}{6}:2\frac{1}{3}\)
\(=\frac{25}{6}:\frac{7}{3}\)
\(=\frac{25}{6}.\frac{3}{7}\)
\(=\frac{25}{14}\)
\(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+10}\)
\(=\frac{1}{\frac{2.3}{2}}+\frac{1}{\frac{3.4}{2}}+\frac{1}{\frac{4.5}{2}}+....+\frac{1}{\frac{10.11}{2}}=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{10.11}\)
\(=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{10.11}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\right)=2\left(\frac{1}{2}-\frac{1}{11}\right)=2.\frac{9}{22}=\frac{9}{11}\)