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A = \(\frac{3^4\left(5.79-1\right)}{2^2.3^2\left(5.79-1\right)}=\frac{9}{4}\); B = \(\frac{3.7.13.37\left(5.11-1\right)}{4.3.7.13.37\left(3.5-1\right)}=\frac{54}{4.14}=\frac{2.9}{4.2.7}=\frac{9}{28}\)
Câu a) \(\dfrac{31995-81}{42660-108}=\dfrac{31914}{42552}=\dfrac{31914:10638}{42552:10638}\)
=\(\dfrac{3}{4}\)
Câu b) \(\dfrac{\left(3.5.7.11.13.15.37-10101\right)}{121212+40404}\)
=\(\dfrac{\left(3.5.7.11.13.15.37-3.7.13.37\right)}{3.7.13.37.12+3.7.13.37.4}\)
=\(\dfrac{3.7.13.37\left(5.11.15-1\right)}{3.7.13.37\left(12+4\right)}\)
= \(\dfrac{824}{16}\)=\(\dfrac{103}{2}\)
\(A=\frac{4157-19}{12471-57}\)\(=\frac{4138}{12414}\)\(=\frac{4138:4138}{12414:4138}\)\(=\frac{1}{3}\)
\(B=\frac{7}{10^2+8.10^2}\)\(=\frac{7}{100+8.100}\)\(=\frac{7}{100+800}\)\(=\frac{7}{900}\)
\(C=\frac{31995}{42660-108}\)\(=\frac{31995}{42552}\)\(=\frac{31995:27}{42552:27}\)\(=\frac{1185}{1576}\)
\(D=\frac{2^{45}.5^3.2^6.3}{8.2^{18}.81.5}=\frac{2^{51}.5^3.3}{2^3.2^{18}.3^4.5}=\frac{2^{51}.5^3.3}{2^{21}.3^4.5}=\frac{2^{30}.5^2}{3^3}\)
k mình nhé.
A=4138/12414=1/3
B=7/900
C=31995/42552=1185/1576
Phần D tui chịu, ahihi
31995 - 81 / 42660 - 108
= 31914 / 42552
= 3.10638 / 4.10638
= 3/4
\(\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times...\times\frac{1000}{999}\)
\(=\frac{3\times4\times5\times...\times1000}{2\times3\times4\times...\times999}=\frac{1000}{2}=500\)
Đặt \(A=\frac{1}{2.2}+\frac{1}{3.3}+.....+\frac{1}{100.100}\)
\(\Rightarrow A< \frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{99.100}\)
\(\Rightarrow A< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{99}-\frac{1}{100}\)
\(\Rightarrow A< 1-\frac{1}{100}\)
\(\Rightarrow A< \frac{99}{100}\)
Mà \(\frac{99}{100}< 1\Rightarrow A< \frac{99}{100}< 1\)
\(\Rightarrow A< 1\)
\(\frac{31995-81}{42660-108}=\frac{3}{4}\)
\(\frac{31995-81}{42660-108}\)
\(=\frac{31914}{42554}\)
\(=\frac{3}{4}\)
Vậy ...........................................