2/6+2/12+2/2+......+2/x+(x+1)=199/201
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Vì: \(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}=0\),nên kết quả bằng 0
a)\(\frac{7}{13}.\frac{7}{15}-\frac{5}{12}.\frac{21}{39}+\frac{49}{21}.\frac{8}{15}\)
=\(\frac{7}{13}.\frac{7}{15}-\frac{5}{12}.\frac{7}{13}+\frac{7}{13}.\frac{8}{15}\)
=\(\frac{7}{13}.\left(\frac{7}{15}-\frac{5}{12}-\frac{8}{15}\right)\)
=\(\frac{7}{13}.\frac{7}{12}\)
=\(\frac{49}{156}\)
b)\(\left(\frac{12}{199}+\frac{23}{200}-\frac{34}{201}\right).\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)
=\(a.\left(\frac{3}{6}-\frac{2}{6}-\frac{1}{6}\right)\)
=a . 0
=0
Bài 2
a)Có
\(3^{200}=3^{2.100}=\left(3^2\right)^{100}=9^{100}\)
\(2^{300}=2^{3.100}=\left(2^3\right)^{100}=8^{100}\)
Vì 8<9 =>\(8^{100}< 9^{100}\) =>\(3^{200}>2^{300}\)
a) \(\frac{7}{13}x\frac{7}{15}-\frac{5}{12}x\frac{21}{39}+\frac{49}{91}x\frac{8}{15}=\frac{7}{13}x\frac{7}{15}-\frac{5}{12}x\frac{7}{13}+\frac{7}{13}x\frac{8}{15}\)
\(=\frac{7}{13}x\left(\frac{7}{15}-\frac{5}{12}+\frac{8}{15}\right)=\frac{7}{13}x\left(1-\frac{5}{12}\right)=\frac{7}{13}x\frac{7}{12}=\frac{49}{156}\)
b) \(\left(\frac{12}{199}+\frac{23}{200}-\frac{34}{201}\right)x\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)=\left(\frac{12}{199}+\frac{23}{200}-\frac{34}{201}\right)x0=0\)
Bài 2:
a) \(0,5+\left(x-\frac{15}{2}\right):\frac{1}{2}=\frac{9}{2}\)
\(\left(x-\frac{15}{2}\right):\frac{1}{2}=4\)
\(x-\frac{15}{2}=2\)
x = 19/2
b) \(2012\times x-2010\times x=2014\)
\(x\times\left(2012-2010\right)=2014\)
\(x\times2=2014\)
x = 1007
c) ( x + 1) + (x+2) + (x+3)+...+(x+100) = 5750
\(x\times100+\left(1+2+3+...+100\right)=5750\)
\(x\times100+5050=5750\)
\(x\times100=700\)
x = 7
\(\left(\frac{12}{199}+\frac{23}{200}-\frac{34}{201}\right)\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)
\(=\left(\frac{12}{199}+\frac{23}{200}-\frac{34}{201}\right)\left(\frac{6}{12}-\frac{4}{12}-\frac{2}{12}\right)\)
\(=\left(\frac{12}{199}+\frac{23}{200}-\frac{34}{201}\right).0\)
\(=0\)
a/ 35 – 2.1111 + 3. 72
= 35 - 2.1 + 3.49
= 35 - 2 + 147
= 33 + 147
= 180
b/ 5.43 + 2.3 – 81. 2 + 7
= 5.64 + 6 - 162 + 7
= 320 + 6 - 162 + 7
= 326 - 162 + 7
= 164 + 7
= 171
c/ 25 + 2.{12 + 2.[3.(5-2)+1]+1}+1
= 32 + 2.{12 + 2.[3.3+1]+1}+1
= 32 + 2.{12 + 2.10+1}+1
= 32 + 2.{12 + 20 + 1}+1
= 32 + 2.{32+1}+1
= 32 + 2.33 + 1
= 32 + 66 + 1
= 98 + 1
= 99
d/ 17.131 + 69.17
= 17 . (131+69)
= 17 . 200
= 3400
e/ 50 – [30 - (6 - 2)2 ]
= 50 - [30 - 42]
= 50 - 14
= 36
f/ 199 +36 + 201 + 184 + 37
= (199+201)+(36+184)+37
= 400 + 220 + 37
= 657
A = (15-17) - |-3| - [ (-2).3 - (-3)2 ]
A = (-2) - 3 - [ (-6) - 9 ]
A = (-5) - (-15)
A = (-5) + 15
A = 10
B = 418 + [ 418 - (418+2018) ]
B = 418 + [ 418 - 2436 ]
B = 418 + (-2018)
B = -1600
Chúc bạn học tốt!
a) 199+36+201+184+37
= 199+201+36+184+37
=400+220+37
=620+37=657
b)1+3+5+...+103+105 (sử dụng công thức)
= (105+1)x105:2
=106x105:2
=11130:2=5565
Bài 2
a) (x-3):4-15=2
(x-3):4 =2+15
(x-3):4 =17
(x-3) =17x4
x-3 =68
x =68+3
x =71
b) (x-5) x ( 2 x X - 6) =0
có 2 TH
TH1: x-5=0
x =0+5
x =5
TH2: 2.x-6= 0
2.x =0+6
2.x =6
x =6:2
x =3
Sửa đề:
\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x.\left(x+1\right)}=\frac{199}{201}\)
\(\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{x.\left(x+1\right)}=\frac{199}{201}\)
\(2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{199}{201}\)
\(2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{199}{201}\)
\(2.\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{199}{201}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{199}{201}:2\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{199}{402}\)
\(\frac{1}{x+1}=\frac{1}{2}-\frac{199}{402}\)
\(\frac{1}{x+1}=\frac{1}{201}\)
\(\Rightarrow x+1=201\)
\(x=201-1\)
\(x=200\)
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