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-----A=-1/3+1/3^2-1/3^3+-----+1/3^50-1/...
A*1/3 =-1/3^2+1/3^3+--------------------+1/3^5...
--------A=-1/3+1/3^2-1/3^3+...+1/3^50-1...
-------A*1/3 =-1/3^2+1/3^3+..---------...+1/3^51-1/3^...
---------------------------------------...
A+A*1/3=-1/3+0...+0+...0---------------...
A+A*1/3= -1/3-1/3^52
4/3*A= -1/3-1/3^52
Vậy
A= -(1/3+1/3^52)*3/4.
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{50}\right)\)
\(=\left(\frac{2}{2}-\frac{1}{2}\right)\left(\frac{3}{3}-\frac{1}{3}\right)\left(\frac{4}{4}-\frac{1}{4}\right)...\left(\frac{50}{50}-\frac{1}{50}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{49}{50}\)
\(=\frac{1}{50}\)
\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).....\left(1-\frac{1}{50}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{49}{50}\)
\(=\frac{1}{50}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ax2=1x2/1x2x3+1x2/2x3x4+...+1x2/48x49x50
Ax2=1/1x2-1/2x3+1/2x3-1/3x4+...+1/48x49-1/49x50
Ax2=1/1x2-1/49x50
Ax2=1/2-1/2450
Ax2=1225/2450-1/2450
Ax2=1224/2450
A=1224/2450:2
A=1224/2450X1/2
A=1224/4900
A=306/1225
![](https://rs.olm.vn/images/avt/0.png?1311)
\(S=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{49.50}\)
\(S=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\)
\(S=1-\dfrac{1}{50}\)
\(S=\dfrac{49}{50}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
So sánh tổng : S = 1/5 + 1/9 + 1/10 + 1/41 + 1/42 với 1/2
S=
=50/50+50/49+50/48+...+50/2
=50.(1/50+1/49+1/48+...+1/4+1/3+1/2)
=50
P=
P=(1/49+1)+(2/48+1)+...+(48/2+1)+1
P= 50/49+50/48+....+50/2+50/50=1
vậy s/p = 1/50
Ta có:
\(P=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\cdot\cdot\cdot\left(1-\frac{1}{50}\right)\)
Suy ra: \(P=\frac{1}{2}\cdot\frac{2}{3}\cdot...\cdot\frac{49}{50}=\frac{1}{50}\)