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71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79
= ( 71 + 79 ) + ( 72 + 78 ) + ( 73 + 77 ) + ( 74 + 76 ) + 75
= 150 + 150 + 150 + 150 + 75
= 150 x 4 + 75
= 600 + 75
= 675
Tìm x :
X x 7 + X x 2 = 108
X x ( 7 + 2 ) = 108
X x 9 = 108
X = 108 : 9
X = 12
\(71+72+73+74+75+76+77+78+79\)
\(=\left(71+79\right)+\left(72+78\right)+\left(73+77\right)+\left(74+76\right)+75\)
\(=150+150+150+150+75\)
\(=600+75\)
\(=675\)
\(X\)x\(7+X\)x\(2=108\)
\(X\)x\(\left(7+2\right)=108\)
\(X\)x\(9=108\)
\(X=108:9\)
\(X=12\)
Vậy \(X=12\)
A = 1 + 1/110 + 1 + 1/90 + ... + 1 + 1 /2
A = 10 + 1/1.2+ 1 /2.3 + ... + 1/9.10 + 1/10.11
A = 10 + 1/1 - 1/2 + 1 /2 - 1/3 + ... + 1/9 - 1/10 + 1/10 - 1/11
A = 10 + 1/1 - 1/11
A = 10 + 10/11
A = 120/11
A = \(\frac{111}{110}+\frac{91}{90}+\frac{73}{72}+...+\frac{13}{12}+\frac{7}{6}+\frac{3}{2}\)
A = \(\left(\frac{1}{2}+1\right)+\left(\frac{1}{6}+1\right)+\left(\frac{1}{12}+1\right)+....+\left(\frac{1}{110}+1\right)\)
A = (1 + 1 + 1 +...+ 1) + \(\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)\)
A = 10 + \(\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)\)
A = \(10+\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)\)
A = \(10+\left(1-\frac{1}{11}\right)\)
A = \(10+\frac{10}{11}\)
A = \(\frac{120}{11}\)
\(=\left(1-\dfrac{1}{2}\right)+\left(1-\dfrac{1}{6}\right)+\left(1-\dfrac{1}{12}\right)+...+\left(1-\dfrac{1}{90}\right)\\ =\left(1+1+...+1\right)-\left(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{90}\right)\\ =9-\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{9\cdot10}\right)\\ =9-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\\ =9-\left(1-\dfrac{1}{10}\right)=9-\dfrac{9}{10}=\dfrac{81}{10}\)
A=1/2+ 5/6 + 11/12 + 19/20 + 29 30 + 41/42 + 55/56 + 71/72 + 89/90
\(A=7+7+7^2+...+7^{100}\)
\(7A=7^2+7^2+7^3+...+7^{101}\)
\(A=14+7^2+7^{101}\)
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