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Bài 1:
\(A=\frac{1}{\left(1+2\right)}+\frac{1}{\left(1+2+3\right)}+\frac{1}{\left(1+2+3+4\right)}\)\(+\frac{1}{\left(1+2+3+4+5\right)}+...+\)\(\frac{1}{\left(1+2+3+...+10\right)}\)
\(A=\frac{1}{3}+\frac{1}{6}+....+\frac{1}{55}\)
\(A=2\left(\frac{1}{6}+\frac{1}{12}+....+\frac{1}{110}\right)\)
\(A=2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{10}-\frac{1}{11}\right)\)
\(A=2.\left(\frac{1}{2}-\frac{1}{11}\right)\)
\(A=\frac{9}{11}\)
Bài 2 :
2) Tử số = 11 x 13 x 15 + 3 x 3 x 3 x 11 x 13 x 15 + 5 x 5 x 5 x 11 x 13 x 15 + 9 x 9 x 9 x 11 x 13 x 15
= (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) x 11 x 13 x 15 = (1+27+125+ 729) x 11 x 13 x 15
Mẫu số = 11 x 13 x 17 + 3 x 3 x 3 x 13 x 15 x 19 + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17 lớn hơn 11 x 13 x 15 + 3 x 3 x 3 x 13 x 15 x 17 + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17
= (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) 13 x 15 x 17 = (1+27+125+729) x 13 x 15 x 17
\(\Rightarrow A< \frac{\left(1+27+125+729\right)\times11\times13\times15}{\left(1+27+125+729\right)\times13\times15\times17}\)
\(=\frac{11}{17}\)
\(=\frac{1111}{1717}=B\)
Vậy \(A=B\)
1)\(A=\frac{1}{3}+\frac{1}{6}+...+\frac{1}{55}=2\left(\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)=2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)=2.\left(\frac{1}{2}-\frac{1}{11}\right)=\frac{9}{11}\)
2) Tử số = 11 x 13 x 15 + 3 x 3 x 3 x 11 x 13 x 15 + 5 x 5 x 5 x 11 x 13 x 15 + 9 x 9 x 9 x 11 x 13 x 15
= (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) x 11 x 13 x 15 = (1+27+125+ 729) x 11 x 13 x 15
Mẫu số = 11 x 13 x 17 + 3 x 3 x 3 x 13 x 15 x 19 + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17
lớn hơn 11 x 13 x 15 + 3 x 3 x 3 x 13 x 15 x 17 + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17
= (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) 13 x 15 x 17 = (1+27+125+729) x 13 x 15 x 17
=> \(A<\frac{\left(1+27+125+729\right)\times11\times13\times15}{\left(1+27+125+729\right)\times13\times15\times17}=\frac{11}{17}=\frac{1111}{1717}=B\)
Vậy A < B
a. = 267 + 864 - 263 - 860
= (267 - 263) + (864 - 860)
= 4 + 4
= 8
b. = [(257 + 37) x 35] : 60
= [294 x 35] : 60
= 10290 : 60
= 171,5
a. ( x - 5 ) : 75 = 125
( x - 5 ) = 125 x 75
x - 5 = 9375
x = 9375 + 5
x = 9380
b. 64 x 8 - 34 x X = 444
512 - 34 x X = 444
34 x X = 512 - 444
34 x X = 68
X = 68 : 34
X = 2
c. 1482 : x + 23 = 80
1482 : x = 80 - 23
1482 : x = 57
x = 1482 : 57
x = 26
d. 126 - 3 x ( X + 2 ) = 15
3 x ( X + 2 ) = 126 - 15
3 x ( X + 2 ) = 111
3 x X + 2 = 111
X + 2 = 111 : 3
X + 2 = 37
X = 37 - 2
X = 35
Chúc bạn hok tốt !
a) ( x - 5 ) : 75 = 125
x - 5 = 125 x 75
x - 5 = 9375
x = 9375 + 5
x = 9380
\(X\%:3+45\%=0,7\\ \Leftrightarrow\dfrac{x}{100}:3+\dfrac{9}{20}=\dfrac{7}{10}\\ \Leftrightarrow\dfrac{x}{100}\times\dfrac{1}{3}=\dfrac{7}{10}-\dfrac{9}{20}\\ \Leftrightarrow\dfrac{x}{300}=\dfrac{14-9}{20}\\ \Leftrightarrow\dfrac{x}{300}=\dfrac{5}{20}\\ \Leftrightarrow x=\dfrac{300\times5}{20}=75\)
Vậy \(x=75\)
a) x + 2,57 = 14,25 - 6,3
=> x + 2,57 = 7,95
=> x = 7,95 - 2,57
=> x = 5,38
Vậy x = 5,38
b) 12,9 - x = 4,2 + 2,4
=> 12,9 - x = 6,6
=> x = 12,9 - 6,6
=> x = 6,3
Vậy x = 6,3
c) x . 93 + x . 0,7 = 100
=> x . (93 + 0,7) = 100
=> x . 93,7 = 100
=> x = 100 : 93,7
=> x = 1000/937
Vậy x = 1000/937
a) \(x+2,57=14,25-6,3\)
\(x+2,57=7,95\)
\(x=7,95-2,57\)
\(\Rightarrow x=5,38\)
b) \(12,9-x=4,2+2,4\)
\(12,9-x=6,6\)
\(x=12,9-6,6\)
\(\Rightarrow x=6,3\)
c) \(x.93+x.0,7=100\)
\(x\left(93+0,7\right)=100\)
\(x.93,7=100\)
\(x=100:93,7\)
\(\Rightarrow x=\frac{1000}{937}\)
d) \(\frac{x}{5}=\frac{4}{2}\)
Ta có: \(x.2=4.5\)
\(x.2=20\)
\(x=20:2\)
\(\Rightarrow x=10\)
B
b