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\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{x.\left(x+1\right)}=\dfrac{499}{500}\)
\(\Leftrightarrow1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{499}{500}\)
\(\Leftrightarrow1-\dfrac{1}{x+1}=\dfrac{499}{500}\)
\(\Leftrightarrow x=499\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Tìm x
190−(x−1)2=189
(x - 1) 2 = 190 - 189
(x - 1) 2 = 1
x = 1+2
x = 2
a, cái câu trả lời trước mk ghi sai
190 - (x-1)2 = 189
(x - 1 ) 2 = 190 - 189
(x-1)2 = 1
x = 1+1
x = 2
![](https://rs.olm.vn/images/avt/0.png?1311)
dấu bằng của mk bt liệt nên bạn thông cảm
A bằng (1.2.3.4).(1.2.3.4)/(1.2.3.4).(2.3.4.5) bằng 5
rút gọn cho nhau bạn nhé
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a: \(\Leftrightarrow3\cdot5^n\cdot25+4\cdot5^n\cdot\dfrac{1}{125}=19\cdot5^{10}\)
\(\Leftrightarrow5^n\cdot\left(75+\dfrac{4}{125}\right)=19\cdot5^{10}\)
\(\Leftrightarrow5^n\simeq2472903,228\)(vô lý)
b: \(\Leftrightarrow6^x\cdot11\cdot\dfrac{1}{6}+2\cdot6^x\cdot6=11\cdot6^{11}+2\cdot6^{11}\cdot36\)
\(\Leftrightarrow6^x\left(\dfrac{11}{6}+12\right)=6^{11}\cdot83\)
\(\Leftrightarrow6^x=6^{12}\)
hay x=12
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a) 210:[16+3.(6+3.2^2)]-3
=210:[16+3.(6+3.4)]-3
=210:[16+3.(6+12)]-3
=210:[16+3.18]-3
=210:[16+54]-3
=210:70-3
=3-3
=0
\(500-\left\{5.\left[409.\left(2^3.3-21\right)^2\right]\right\}-3\)
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1) 22.25.17.+5.20.27+102.56
=4.25.17+5.20.27+100.56
=100.17+100.27+100.56
=100(17+27+56)
=100.100
=10000
2) 132-[116-(132-1282)]
=132-[116-(132-16384)]
=132-[116-(-16252)]
=132-(116+16252)
=132-16368
=-16236
3) 4.52-81:32
=4.25-34:32
=100-34-2
=100-32
=100-9
=91
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a) \(113.15-13.15+\left(-500\right)=15.\left(113-13\right)+\left(-500\right)\)
\(=15.100+\left(-500\right)\)
\(=1500+\left(-500\right)\)
\(=1000\)
c) \(\left(3x-12\right):2=4^2.3\)
\(\left(3x-12\right):2=16.3\)
\(3x-12=16.3.2\)
\(3x-12=96\)
\(3x=108\)
\(x=36\)
d) \(25-\left|x\right|=12\)
\(\left|x\right|=25-12\)
\(\left|x\right|=13\)
\(\Rightarrow x\in\left\{-13;13\right\}\)
b) \(\left(3^2.5-60:2^2\right)-20.10^0=\left(9.5-60:4\right)-20.1\)
\(=\left(45-15\right)-20\)
\(=30-20\)
\(=10\)
Lưu ý: -Dấu "." là dấu nhân
- Đề bài này là đúng (đã trao đổi với Nguyễn Phương Thảo 2008)