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a,
( 18.38 + 16.76 - 1 ) = ( 39 x 19 + 64 x 20 - 65 )x
=> ( 684 + 1216 - 1) = ( 741 + 1280 - 65 )x
=> 1899 = 1956x
=> 1956x = 1899
=> x = 1899/1956
=> x = 633/652
Tương tự tiếp...
( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) + ( x + 5 ) = 65
( x + x + x + x + x ) + ( 1 + 2 + 3 + 4 = 5 ) = 65
x * 5 +15 = 65
x * 5 = 65 - 15
x * 5 = 50
x = 50 : 5
x = 10
( X + 1 ) + ( X + 2 ) + ( X + 3 ) + ( X + 4 ) + ( X + 5 ) = 65
X x 5 + ( 1 + 2 + 3 + 4 + 5 ) = 65
X x 5 + 15 = 65
X x 5 = 65 - 15
X x 5 = 50
X = 50 : 5
X = 10
(x+1) + ( x+2) + (x+3) + (x+4) + ( x+5)= 65
(x+x+x+x+x)+(1+2+3+4+5)=65
x*5+15=65
x*5=65-15
x*5=50
x=10
<=>(x+x+x+x+x)+(1+2+3+4+5)=65
=>5x+15=65
=>5x=65-15
=>5x=50
=>x=50:5
=>x=10
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
20,10x35-19,45x65+20,10x65-19,45x35
=(35+65)x20,10+(35+65)x19,45
=100x20,10-100x19,45
=100x(20,10-19,45)
=100x0,65=65
18 x 38 + 16 x 38 x 2 -1 = (18 x 2 x 19 + 32 x 2 x 20 - 32 x 2 - 1) x X
X = (18 x 38 + 32 x 38 - 1) : (18 x 38 + 32 x 38 - 1)
X = 1