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\(=\frac{1}{50}-\frac{1}{51}+\frac{1}{51}-\frac{1}{52}_{ }+.....-\frac{1}{98}+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)
\(=\frac{1}{50}+\left(\frac{-1}{51}+\frac{1}{51}\right)+.....+\left(\frac{-1}{98}+\frac{1}{98}\right)+\left(\frac{-1}{99}+\frac{1}{99}\right)-\frac{1}{100
}\)
\(=\frac{1}{50}+0+0+....+0+0-\frac{1}{100}\)
\(=\frac{1}{50}-\frac{1}{100
}\)
\(=\frac{1}{100}\)
Nhớ **** cho mình nhé
![](https://rs.olm.vn/images/avt/0.png?1311)
\(B=\left(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{50\cdot51}\right)+\left(\dfrac{5}{6}+\dfrac{19}{20}+...+\dfrac{2549}{2550}\right)\)
\(B=\left(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+..+\dfrac{1}{50\cdot51}\right)+\left(1-\dfrac{1}{2\cdot3}\right)+\left(1-\dfrac{1}{3\cdot4}\right)+...+\left(1-\dfrac{1}{50\cdot51}\right)\)
\(B=\left(1+1+...+1\right)+\left(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{50\cdot51}\right)-\left(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{50\cdot51}\right)\)
\(B=1\cdot49=49\) (vì có (50 - 2) : 1 + 1 = 49 số hạng 1)
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\(\frac{1}{4.5}+\frac{1}{5.6}+.....+\frac{1}{99.100}\)
=\(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+.....+\frac{1}{99}-\frac{1}{100}\)
=\(\frac{1}{4}-\frac{1}{100}\)
=\(\frac{6}{25}\)
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Đặt A = 1/1x2 + 1/2x3 + 1/3x4 + .... + 1/99x100
=> A = 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + .... + 1/99 - 1/100
=> A = 1 - 1/100
=> A = 99/100
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\(M=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{99\times100}\)
\(M=\left(\frac{1}{1}-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+...+\left(\frac{1}{99}-\frac{1}{100}\right)\)
\(M=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(M=\frac{1}{1}-\frac{1}{100}\)
\(M=\frac{100}{100}-\frac{1}{100}\)
\(M=\frac{99}{100}\)
\(M=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{99\times100}\)
\(M=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{100}-\frac{1}{100}\)
\(M=1-\frac{1}{100}\)
\(M=\frac{99}{100}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A=1/1x2+1/2x3+.....+1/99x100
A=1/1-1/2+1/2-1/3+...+1/99-1/100
A=1/1 - 1/100
A=99/100
ta có: A=1/1x2+1/2x3+...+1/99x100
A=1-1/2+1/2-1/3+...+1/99-1/100
A=1-1/100
A=99/100
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1/1×2 + 1/2×3 + 1/3×4 + 1/4×5 + ... + 1/99×100
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/99 - 1/100
= 1 - 1/100
= 99/100
1/50x51+1/51x52+...+1/99x100=1/50-1/51+1/51 - 1/52+.....+1/99 - 1/100
=1/50-1/100
= 2/100-1/100
=1/100
Nha bạn
=1/50-1/100
= 1/100
Nha bạn