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\(\dfrac{5}{13}\times\dfrac{7}{11}+\dfrac{5}{13}\times\dfrac{2}{11}+\dfrac{8}{13}\times\dfrac{9}{11}\)
\(=\dfrac{5}{13}\times\left(\dfrac{7}{11}+\dfrac{2}{11}\right)+\dfrac{8}{13}\times\dfrac{9}{11}\)
\(=\dfrac{5}{13}\times\dfrac{9}{11}+\dfrac{8}{13}\times\dfrac{9}{11}\)
\(=\dfrac{9}{11}\times\left(\dfrac{5}{13}+\dfrac{8}{13}\right)\)
\(=\dfrac{9}{11}\times1\)
\(=\dfrac{9}{11}\)
a) \(20,23\times21+20,23\times80-20,23\)
\(=20,23\times\left(21+80-1\right)\)
\(=20,23\times100\)
\(=2023\)
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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 \(A=B\)
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Ta có : A=20/11×13 + 20/13×15 +20/15×17+...+20/53×55
A = 10 ×( 2/11×13+2/13×15+...12/53×55)
A = 10 ×(1/11-1/13+1/13-1/15+1/15-1/17+...+1/53-1/55)
A = 10 × (1/11-1/55)
A =10 × 4/55
A = 8/11
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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
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\(\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}+...+\frac{2}{13\times15}\)
\(=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{13}-\frac{1}{15}\)
\(=\frac{1}{5}-\frac{1}{15}\)
\(=\frac{2}{15}\)
= 2 x (1/ 5 x 7 + 1/ 7 x 9 + ... + 1/ 13 x 15)
= 2 x (1/5 - 1/7 + 1/7 - 1/9 + ... + 1/13 - 1/15)
= 2 x (1/5 - 1/15)
= 2 x (3/15 - 1/15)
= 2 x 2/15
= 4/15
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a) 3/5x7/9+11/9x3/5
=3/5 x(7/9+11/9)
= 3/5x2
=6/5
b)14/13:1/2+3/13x2-2x7/13
= 14/13 x 2 +3/13 x2 - 2x7/13
=2 x (14/13 +3/13 -7/13)
= 2 x 10/13
= 20/13
a) 3/5 x 7/9 + 11/9 x 3/5 - 3/10
= 3/5 x 7/9 + 11/9 x 3/5 - 3/5 x 2
= 3/5 x ( 7/9 + 11/9 - 2 )
= 3/5 x 0
= 0
b) 14/13 : 1/2 + 3/13 x 2 - 2 x 7/13
= 14/13 x 2/1 + 3/13 x 2 - 2 x 7/13
= ( 14/13 + 3/13 - 7/13 ) x 2
= 10/13 x 2 = 20/13
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142+21-98+1+2+3+4+5+6+7+8+9x0=
= 1/9 - 1/11 + 1/11 - 1/13 +........+1/151 - 1/153
= 1/9 - 1/153
=16/153