so sánh A và B biết
A=11.13.15+33.39.45+55.65.75+99.117.135 / 11.1.17+39.45.51+65.75.85+117.135.
153
B=1111/1717
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Cho phép mình làm bài này theo cái đề do bạn Nguyễn Bảo Trung chữa lại nhé Nguyễn Lê Ngọc Thanh
\(A=\dfrac{11\cdot13\cdot15+33\cdot39\cdot45+55\cdot65\cdot75+99\cdot117\cdot135}{13\cdot15\cdot17+39\cdot45\cdot51+65\cdot75\cdot85+117\cdot135\cdot153}\text{ và }B=\dfrac{1111}{1717}\\ \)
\(\text{Ta có : }\)
\(A=\dfrac{11\cdot13\cdot15+33\cdot39\cdot45+55\cdot65\cdot75+99\cdot117\cdot135}{13\cdot15\cdot17+39\cdot45\cdot51+65\cdot75\cdot85+117\cdot135\cdot153}\\ A=\dfrac{11\cdot13\cdot15+3\cdot11\cdot13\cdot15+5\cdot11\cdot13\cdot15+9\cdot11\cdot13\cdot15}{13\cdot15\cdot17+3\cdot13\cdot15\cdot17+5\cdot13\cdot15\cdot17+9\cdot13\cdot15\cdot17}\\ A=\dfrac{11\cdot13\cdot15\left(1+3+5+9\right)}{13\cdot15\cdot17\left(1+3+5+9\right)}\\ A=\dfrac{11}{17}\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\left(1\right)\)
\(B=\dfrac{1111}{1717}\\ B=\dfrac{11\cdot101}{17\cdot101}\\ B=\dfrac{11}{17}\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\left(2\right)\)
Từ \(\left(1\right)\) và \(\left(2\right)\) suy ra :
\(A=B=\dfrac{11}{17}\)
\(\Rightarrow A=B\)
Vậy \(A=B\)
Bn ơi , mik nghĩ mẫu số của A có cái 11.13.17 phải là 13.15.17
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
a)3200=(32)100=9100
2300=(23)100=8100
vì 9>8 nên 9100>8100
hay 3200>2300
b)\(A=\frac{121212}{171717}+\frac{2}{17}-\frac{404}{1717}=\frac{12.10101}{17.10101}+\frac{2}{17}-\frac{4.101}{17.101}=\frac{12}{17}+\frac{2}{17}-\frac{4}{17}\)
\(=\frac{10}{17}=B\)
Vậy A=B
a) Ta có: 3200 = ( 32 )100 = 9100
2300 = ( 23 )100 = 8100
Vì 9 > 8 nên 9100 > 8100.
Vậy 3200 > 2300
b) \(A=\frac{121212}{171717}+\frac{2}{17}-\frac{404}{1717}=\frac{12}{17}+\frac{2}{17}-\frac{4}{17}=\frac{12+2-4}{17}=\frac{10}{17}=B\)
Vậy A = B