P=1x2 2x3 3x4 ... 29x30
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Ax3= 1x2x3 + 2x3x3+.....+29x30x3
lấy B= 1x2x3+ 2x3x4+......+29x30x31
B- Ax3= 0 + 1x2x3+ 2x3x4+ 28x29x30= B- 29x30x31. Suy ra Ax3= 29x30x31
![](https://rs.olm.vn/images/avt/0.png?1311)
Ax3= 1x2x3 + 2x3x3+.....+29x30x3 lấy B= 1x2x3+ 2x3x4+......+29x30x31 B- Ax3= 0 + 1x2x3+ 2x3x4+ 28x29x30= B- 29x30x31. Suy ra Ax3= 29x30x31
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\(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+....+\frac{1}{29\times30}\)
=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{29}-\frac{1}{30}\)
=\(\frac{1}{2}-\frac{1}{30}=\frac{15}{30}-\frac{1}{30}=\frac{14}{30}=\frac{7}{15}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{20}\)
\(=\frac{1}{2}-\frac{1}{20}=\frac{10}{20}-\frac{1}{20}=\frac{9}{20}\)
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\(3S=1\times2\times3+2\times3\times3+...+29\times30\times3\\ 3S=1\times2\times\left(3-0\right)+2\times3\times\left(4-1\right)+...+29\times30\times\left(31-28\right)\\ 3S=1\times2\times3-1\times2\times3+2\times3\times4-...-28\times29\times30+29\times30\times31\\ 3S=29\times30\times31\\ S=29\times10\times31=8990\)
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\(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+....+\dfrac{1}{24\times25}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{24}-\dfrac{1}{25}\)
\(=1-\dfrac{1}{25}\)
\(=\dfrac{24}{25}\)
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P = 1.2 + 2.3+ 3.4 +.....+29.30
3P = 1.2.3 +2.3.3 +3.4.3 +....+29.30.3
3P = 1.2.3 + 2.3.(4-1) + 3.4.(5-2) +......+29.30.(31-28)
3P = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + 3.4.5 +.....-28.29.30 + 29.30.31
3P = 29.30.31
p = 29.30.31: 3
P = 8990