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       \(\frac{25}{26}\times\frac{26}{27}\times\frac{27}{28}\times\frac{28}{29}\times\frac{29}{30}\)

\(=\frac{25\times26\times27\times28\times29}{26\times27\times28\times29\times30}\)

\(=\frac{25}{30}\)

\(=\frac{5}{6}\)

BÀI NÀY TÍNH BẰNG CÁCH LOẠI BỎ NHỮNG SỐ GIỐNG NHAU Ở TRÊN TỬ VÀ DƯỚI MẪU 

\(\frac{25}{26}\times\frac{26}{27}\times\frac{27}{28}\times\frac{28}{29}\times\frac{29}{30}\)

\(=\frac{25}{30}\)

\(=\frac{5}{6}\)

1) $(-35)\cdot18+28\cdot35$

$=35\cdot(-18)+28\cdot35$

$=35\cdot(-18+28)$

$=35\cdot10$

$=350$

2) $53\cdot29-47\cdot(-29)$

$=53\cdot29-47\cdot(-1)\cdot29$

$=53\cdot29+47\cdot29$

$=29\cdot(53+47)$

$=29\cdot100$

$=2900$

3) $125\cdot(-24)+24\cdot225$

$=(-125)\cdot24+24\cdot225$

$=24\cdot(-125+225)$

$=24\cdot100$

$=2400$

4) $26\cdot(-121)-121\cdot(-36)$

$=-121\cdot[26+(-36)]$

$=-121\cdot(26-36)$

$=-121\cdot(-10)$

$=121\cdot10$

$=1210$

5) $65\cdot(-25)+25\cdot(-23)$

$=-65\cdot25+25\cdot(-23)$

$=25\cdot(-65-23)$

$=25\cdot(-88)$

$=-2200$

6) $237\cdot(-26)+26\cdot137$

$=-237\cdot26+26\cdot137$

$=26\cdot(-237+137)$

$=26\cdot(-100)$

$=-2600$

7) $30\cdot(-125)+25\cdot30$

$=30\cdot(-125+25)$

$=30\cdot(-100)$

$=-3000$

8) $(-37)\cdot69+(-31)\cdot37$

$=37\cdot(-69)+37\cdot(-31)$

$=37\cdot(-69-31)$

$=37\cdot(-100)$

$=-3700$

9) $31\cdot72-31\cdot70-31\cdot2$

$=31\cdot(72-70-2)$

$=31\cdot(2-2)$

$=31\cdot0$

$=0$

10) $(-12)\cdot47+(-12)\cdot52+(-12)$

$=-12\cdot(47+52+1)$

$=-12\cdot100$

$=-1200$

$\text{#}Toru$

a: =34x(-100)=-3400

b: =41(-76-24)=-4100

c: =-24(125-225)=2400

d: =26(-237+137)=-2600

e: =25(-63+23)=25x(-40)=-1000

a; (-13).34 - 87.34

= 13.34 - 87.34

=   -34.(13+ 87)

= - 34.100

= 3400

b; 74.(-41) - 41.26

= -74.41 - 41.26

= - 41.(74 + 26)

= - 41.100

= - 4100 

c; 125.(-24) + 24.125

= 24.(- 125  + 225)

= 24.100

= 2400

d; 237.(-26) + 26.137

= -26.(237 - 137)

= -26. 100

= -2600

a)26+3x26+26+26x2

=26x1+26x3+26x1+26x2

=26x(1+3+1+2)

=26x7=182

Đặt : \(A=\frac{1}{20.23}+\frac{1}{23.26}+\frac{1}{26.29}+...+\frac{1}{77.80}\)

\(\Rightarrow3A=\frac{3}{20.23}+\frac{3}{23.26}+\frac{3}{26.29}+...+\frac{3}{77.80}\)

\(\Rightarrow3A=\frac{1}{20}-\frac{1}{23}+\frac{1}{23}-\frac{1}{26}+\frac{1}{26}-\frac{1}{29}+...+\frac{1}{77}-\frac{1}{80}\)

\(\Rightarrow3A=\frac{1}{20}+\left(\frac{1}{23}-\frac{1}{23}\right)+\left(\frac{1}{26}-\frac{1}{26}\right)+...+\left(\frac{1}{77}-\frac{1}{77}\right)-\frac{1}{80}\)

\(\Rightarrow3A=\frac{1}{20}-\frac{1}{80}\)

\(\Rightarrow3A=\frac{3}{80}\)

\(\Rightarrow A=\frac{3}{80}:3\)

\(\Rightarrow A=\frac{1}{80}\)

Vì 80 > 79 nên \(\frac{1}{80}< \frac{1}{79}\)hay \(A< \frac{1}{79}\)

~ Hok tốt ~

Ta có :

\(\frac{1}{20.23}+\frac{1}{23.26}+...+\frac{1}{77.80}\)

\(=\frac{1}{3}\left(\frac{3}{20.23}+\frac{3}{23.26}+...+\frac{3}{77.80}\right)\)

\(=\frac{1}{3}\left(\frac{1}{20}-\frac{1}{23}+\frac{1}{23}-\frac{1}{26}+...+\frac{1}{77}-\frac{1}{80}\right)\)

\(=\frac{1}{3}\left(\frac{1}{20}-\frac{1}{80}\right)\)

\(=\frac{1}{3}.\frac{3}{80}\left(\frac{3}{80}< 1\right)\)

\(\Leftrightarrow\frac{1}{20.23}+\frac{1}{23.26}+...+\frac{1}{77.80}< \frac{1}{3}\left(đpcm\right)\)

\(M=\frac{1}{20.23}+\frac{1}{23.26}+\frac{1}{26.29}+...+\frac{1}{77x80}\)

\(M=\frac{1}{20}-\frac{1}{23}+\frac{1}{23}-\frac{1}{26}+\frac{1}{26}-\frac{1}{29}+...+\frac{1}{77}-\frac{1}{80}\)

\(M=\frac{1}{20}-\frac{1}{80}=\frac{3}{80}\)

\(\frac{3}{80}=\frac{3x9}{80x9}=\frac{27}{720};\frac{1}{9}=\frac{1x80}{9x80}=\frac{80}{720}\)

Vì \(\frac{27}{720}< \frac{80}{720}\Rightarrow\frac{3}{80}< \frac{1}{9}\Rightarrow M< \frac{1}{9}\)

          #~Will~be~Pens~#

Hoàng Nguyên Hiếu:Sai rồi nha bạn

\(\frac{1}{20.23}=\frac{1}{20}-\frac{1}{23}\Leftrightarrow23-20=1\)

-.-