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\(\frac{13.\left(37-1\right)}{12\left(2+37\right)}=\frac{13.36}{12.39}=\frac{13.4.3.3}{4.3.3.13}=1\)
học tốt nhé
ủng hộ nhé
\(\frac{37.13-13}{24+37.12}=\frac{37.12+37-13}{24+37.12}=\frac{37.12+\left(37-13\right)}{24+37.12}=\frac{37.12+24}{24+37.12}=1\)

a, 37.12=37.3.4=111.4=444
b, 15873.21= 15873. 7. 3= 111111. 3= 333333
a, Ta có: 37 . 3 = 111
mà \(12=3.4\)
\(\Rightarrow37.12=37.3.4=111.4=444\)
b, Ta có: 15873.7 = 111111
mà \(21=7.3\)
\(\Rightarrow15873.21=15873.7.3=111111.3=333333\)


Bài 1:
\(\frac{37.13-13}{24+37.12}=\frac{13.\left(37-1\right)}{2.12+37.12}=\frac{13.36}{12.\left(37+2\right)}=\frac{13.36}{12.39}=\frac{1.3}{1.3}=1\)
Bài 2:
\(\frac{101+100+...+2+1}{101-100+99-98+...+3-2+1}=\frac{\left[\left(101-1\right):1+1\right].\left(101+1\right):2}{\left(101-100\right)+\left(99-98\right)+...+\left(3-2\right)+1}\)\(=\frac{101.102:2}{1.\left[\left(101-1\right):2+1\right]}=\frac{5151}{1.51}=\frac{5151}{51}=101\)
\(\frac{3737.43-4343.37}{2+4+...+100}=\frac{37.101.43-43.101.37}{2+4+...+100}=\frac{0}{2+4+6+...+100}=0\)

Xét tử số:
=37.13 - 13.1
= 13. (37-1) = 13.36
Xét mẫu số:
=12.2+37.12
=12.(37+2) = 12.39
\(\frac{13.36}{12.39}=\frac{13.12.3}{12.3.13}=1\)
(sau khi đã rút gọn)
xét tử số:
=37,13-13,1
=13x(37-1)
=13,36
xét mẫu số:
=12,2+37,12
=12x(37+2)
=12,39\(\frac{13,26}{12,39}=\frac{12.12.3}{12.3.13}=1\)


B = 1 + 2\(^2\) + 2\(^4\) + ... + 2\(^{2024}\) + 2\(^{2026}\)
2\(^2\) B = 2\(^2\) + 2\(^4\) + ...+ \(2^{2026}\) + 2\(^{2028}\)
4B - B = 2\(^2\) + 2\(^4\) + ...+ \(2^{2026}\) + 2\(^{2028}\) - 1 - 2\(^2\) - 2\(^4\) - ... - 2\(^{2024}\) - 2\(^{2026}\)
3B = (2\(^2\) - 2\(^2\)) + (2\(^4\) - 2\(^4\)) +...+ (2\(^{2026}\) - \(2^{2026}\)) + (2\(^{2028}\) - 1)
3B = 0 + 0 +... + 0 + 2\(^{2028}\) - 1
3B = 2\(^{2028}\) - 1
B = \(\frac{2^{2028}-1}{3}\)
Ta có: \(B=1+2^2+2^4+\cdots+2^{2024}+2^{2026}\)
=>\(4B=2^2+2^4+2^6+\ldots+2^{2026}+2^{2028}\)
=>\(4B-B=2^2+2^4+2^6+\cdots+2^{2026}+2^{2028}-1-2^2-\cdots-2^{2026}\)
=>\(3B=2^{2028}-1\)
=>\(B=\frac{2^{2028}-1}{3}\)

a) \(1\dfrac{13}{15}.\left(-5\right)^2.3+\left(\dfrac{8}{15}-\dfrac{19}{60}\right):1\dfrac{23}{24}\)
\(=\dfrac{28}{15}.25.3+\dfrac{13}{60}.\dfrac{24}{47}\)
\(=140+\dfrac{26}{235}=140\dfrac{26}{235}\)
b) \(\dfrac{\left(\dfrac{11^2}{200}+0,414:0,01\right)}{\dfrac{1}{12}-37.25+3\dfrac{1}{6}}\)
\(=\dfrac{\left(\dfrac{121}{200}-41,4\right)}{\dfrac{1}{12}-92519+\dfrac{19}{6}}\)
\(=\dfrac{2\dfrac{191}{207}}{-9251575}\)
37.12 + 37 .88 - 137.25 + 37.25
= 37. ( 12 + 88) - 25.( 137 - 37)
= 37. 100 - 25 . 100
= 100.( 37 - 25)
= 100. 12
= 1200
37.12 + 37 .88 - 137.25 + 37.25
= 37. ( 12 + 88) - 25.( 137 - 37)
= 37. 100 - 25 . 100
= 100.( 37 - 25)
= 100. 12
= 1200