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![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)
\(A=\frac{2-1}{1.2}+\frac{3-2}{2.3}+...+\frac{100-99}{99.100}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{100}=\frac{99}{100}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1/1.2+1/2.3+....+1/99.100
=1/1-1/2+1/2-1/3+...+1/99-1/100
=1/1-1/100=100/100-1/100=99/100
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt A=1.2+2.3+3.4+...+99.100
3A=1.2.3+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)
3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100
3A=99.100.101
A=333300
![](https://rs.olm.vn/images/avt/0.png?1311)
A = 1.2 + 2.3 + ... + 99.100
3A = 1.2.3 + 2.3.(4-1) +...+ 99.100.(101-98)
3A = 1.2.3 + 3.2.4 - 1.2.3 + ... + 99.100.101 - 98.99.100
3A = 99.100.101
3A = 999900
A = 3A : 3 = 999900 : 3 = 333300
A = 1.2 + 2.3 + ... + 99.100
3A = 1.2.3 + 2.3.(4-1) + ... + 99.100.(101-98)
3A = 1.2.3 + 2.3.4 - 1.2.3 + ... + 99.100.101 - 98.99.100
3A = 99.100.101
3A = 999900
A = 333300
![](https://rs.olm.vn/images/avt/0.png?1311)
)chứng tỏ
a)1/1x2+1/2x3+...+1/9x10 <1
b)1/1x2+1/2x3+...+1/99x100 <1
a)4/1x5+1/5x9+1/9x13+1/13x17+1/17x21<1
Lưu ý:"x" là phép nhân
Toán lớp 6
ái tích mình tíc lại nhà
CÂU a đề bài nó sao sao đó
mà gợi ý cho bạn ....bạn tính tổng đó ra bao nhiêu rồi đem so sánh cho 1
![](https://rs.olm.vn/images/avt/0.png?1311)
A=1 - 1/2 + 1/2 - 1/3 +...+ 1/99 - 1/100
A=1 - 1/100
A=100/100 - 1/100
A=99/100
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\Leftrightarrow3x-\left(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{99.100}\right)=\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{18.19.20}\right)\)
\(\Leftrightarrow3x-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{99}-\frac{1}{100}\right)=\frac{1}{2}\cdot\left(\frac{1}{1.2}-\frac{1}{2.3}+....+\frac{1}{18.19}-\frac{1}{19.20}\right)\)
\(\Leftrightarrow3x-\left(1-\frac{1}{100}\right)=\frac{1}{2}\cdot\left(\frac{1}{1.2}-\frac{1}{19.20}\right)\)
\(\Leftrightarrow3x-\frac{99}{100}=\frac{1}{2}\cdot\frac{189}{380}\)
\(\Leftrightarrow3x-\frac{99}{100}=\frac{189}{760}\)
\(\Leftrightarrow3x=\frac{189}{760}+\frac{99}{100}=\frac{4707}{3800}\)
\(\Leftrightarrow x=\frac{1569}{3800}\)
\(\text{Vậy }x=\frac{1569}{3800}\)
\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{100}\)
\(A=\frac{99}{100}\)
\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{100}\)
\(A=\frac{99}{100}\)