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a) 151 - 291 : 288 + 12 . 3
= 151 - 23 + 1 . 3
= 151 - 8 + 3
= 143 + 3
= 146
b) 1449 - { [ ( 216 +184 ) : 8 ] . 9 }
= 1449 - { [ 400 : 8 ] . 9 }
= 1449 - { 50 . 9 }
= 1449 - 450
= 999
c) 23 . 75 + 25 . 23 + 180
= 23 . ( 75 + 25 ) + 180
= 23 . 100 + 180
= 2300 + 180
= 2480
d) 80 - ( 4 . 52 - 3 . 23 )
= 80 - ( 4 . 25 - 3 . 8 )
= 80 - ( 100 - 24 )
= 80 - 76
= 4
\(A=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{9^2}< \frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{8\cdot9}\)
\(A=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{9^2}>\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{9\cdot10}\)
Ta có : \(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{8\cdot9}\)
\(=1-\frac{1}{2}+...+\frac{1}{8}-\frac{1}{9}\)
\(=1-\frac{1}{9}=\frac{8}{9}(1)\)
\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{9\cdot10}\)
\(=\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{2}-\frac{1}{10}=\frac{8}{20}=\frac{2}{5}(2)\)
Từ 1 và 2 => \(\frac{8}{9}>A>\frac{2}{5}\)
\(\Rightarrow(đpcm)\)
Ta có: \(\frac{1}{1.2}>\frac{1}{2^2 }\)
\(\frac{1}{2.3}>\frac{1}{3^2}\)
. . .
\(\frac{1}{8.9}>\frac{1}{9^2}\)
\(\Rightarrow\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{8.9}>A\)
\(\Rightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{8}-\frac{1}{9}>A\)
\(\Rightarrow1-\frac{1}{9}>A\)
\(\Rightarrow\frac{8}{9}>A \left(1\right)\)
Ta lại có:
\(\frac{1}{2^2}>\frac{1}{2.3}\)
\(\frac{1}{3^2}>\frac{1}{3.4}\)
. . .
\(\frac{1}{9^2}>\frac{1}{9.10}\)
\(\Rightarrow A>\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)
\(\Rightarrow A>\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)
\(\Rightarrow A>\frac{1}{2}-\frac{1}{10}\)
\(\Rightarrow A>\frac{2}{5}\left(2\right)\)
Từ (1) và (2) => \(\frac{8}{9}>A>\frac{2}{5}\)
Chúc bạn hok tốt !!!
1. Tính:
a) 23 + 24 - ( 65 x 2 - 4 ) x 4 + 66 + 44 - ( 54 : 9 x 9 : 9 + 45 ) : 1 + 1 - 1 x ( 23 + 23 - 23 x 2 +1 ) = 51
b) 4444444444444444444444444444444444444444444444444444444444444444444 : 1
= 4444444444444444444444444444444444444444444444444444444444444444444
c) 30 = 0
d) 1/1 = 1
e)
a) - 530
b) 44444444444444444444444444444444444444444444444444444444444444444444
c) 0
d) 1
e) Em là em
lớp 1=))???
lớp 1 à
???????