Tính nhẩm:
2 x 7 2 x 5 2 x 2 | 2 x 4 2 x 9 2 x 6 | 5 x 5 5 x 7 5 x 3 | 5 x 6 5 x 8 5 x 9 |
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a.35 x 34 + 35 x 38 + 65 x 75 + 45 x 65
= 35 x (34 + 38) + 65 x 75 + 65 x 45
= 35 x 72 + 65 x (75+45)
= 35 x 72 + 65 x 120
= 35 x 72 + 65 x (72 + 48)
= 35 x 72 + 65 x 72 + 65 x 48
= (35+65) x 72 + 65 x 48
= 100 x 72 + 65 x 48
= 7200 + 3120
= 10320
b.39 x 8 + 60 x 2 + 21 x 8
=39 x 8 + 15 x 4 x 2 +21 x 8
= 39 x 8 + 15 x 8 + 21 x 8
=(39 + 15 + 21) x 8
= 75 x 8
= 600
c.58 x 75 + 58 x 50 - 58 + 25
= 58 x 75 + 58 x 50 - 58 x 1 + 25
= 58 x(75+50-1)+25
= 58 x 124 + 25
= 7192 + 25
= 7217
d.125 x 98 - 125 x 46 - 52 x 25
= 25 x 5 x 98 - 25 x 5 x 46 - 25 x 52
= 25 x 490 - 25 x 230 - 25 x 52
= 25 x (490 - 230 - 52)
= 25 x 208
= 5200
A = 78 x 31 + 78 x 24 + 78 x 17 + 22 x 72
A = 78 x ( 31 + 24 + 17 ) + 22 x 72
A = 78 x 72 + 22 x 72
A = 72 x ( 78 + 22 )
A = 72 x 100
A = 7200
C = 53 x 39 + 47 x 39 - 53 x 21 - 47 x 21
C = 39 x ( 53 + 47 ) - 21 x ( 53 - 47 )
C = 39 x 100 - 21 x 6
C = 3900 - 126
C = 3774
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
2 x 7 = 14
2 x 5 = 10
2 x 2 = 4
2 x 4 = 8
2 x 9 = 18
2 x 6 = 12
5 x 5 = 25
5 x 7 = 35
5 x 3 = 15
5 x 6 = 30
5 x 8 = 40
5 x 9 = 45