40404/70707 - 1/14
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2 tháng 4 2018
\(B=\dfrac{40404}{70707}+\dfrac{244\times395-151}{244+395\times243}+\dfrac{1\times3\times5+2\times6\times10+4\times12\times20+7\times21\times35}{1\times5\times7+2\times10\times14+4\times20\times28+7\times35\times49}\\ =\dfrac{4}{7}+\dfrac{243\times395+395-151}{244+395\times243}+\dfrac{1\times3\times5\left(1+2+4+7\right)}{1\times5\times7\left(1+2+4+7\right)}\\ =\dfrac{4}{7}+\dfrac{243\times395+244}{244+395\times243}+\dfrac{3}{7}\\ =\left(\dfrac{4}{7}+\dfrac{3}{7}\right)+1\\ =1+1=2\)
VN
2
1 tháng 4 2016
Ta co:
1/2+1/6+1/12+1/20+1/30+1/42
=1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7
Ta co: 6/7=6.10101/7.10101=60606/70707
Vi 60606/70707=60606/70707 nen 6/7=60606/70707
Vay 1/2+1/6+1/12+1/20+1/30+1/42 = 60606/70707
D
1 tháng 4 2016
ta có:
\(\frac{60606}{70707}=\frac{6}{7}\)
ta có:
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}=\)
\(1-\frac{1}{2}+\frac{1}{2}-...-\frac{1}{7}=\frac{6}{7}\)
suy ra 6/7=6/7
suy ra \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}=\frac{60606}{70707}\)
NT
5
25 tháng 5 2015
Ta có:
\(A=\frac{3.5.7.11.13.37-10101}{1212120+40404}\)
\(=\frac{\left(3.7.11.13.37\right).5-10101.1}{120.10101+4.10101}\)
\(=\frac{10101.\left(5-1\right)}{10101.\left(120+4\right)}\)
\(=\frac{4}{124}=\frac{1}{31}\)
TA
25 tháng 4 2016
Sai rồi:
A = 5.11.(3.7.13.37) - 10101/(10101.120 + 10101.4)
= (5.11.10101 - 10101)/(10101.120+10101.4)
= 10101(5.11-1)/10101(120+4)
= 27/62.
\(\dfrac{40404}{70707}-\dfrac{1}{14}\\ =\dfrac{4\cdot10101}{7\cdot10101}-\dfrac{1}{14}\\ =\dfrac{4}{7}-\dfrac{1}{14}\\ =\dfrac{8}{14}-\dfrac{1}{14}\\ =\dfrac{7}{14}\\ =\dfrac{1}{2}\)