(1-1/2)x(1-1/3)x...x(1-1/99) = ? Ai giúp mình với!!!!!!
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![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{x+1}{99}+\frac{x+2}{99}+\frac{x+3}{99}+\frac{x+4}{99}=-4\)
=>\(\frac{\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+\left(x+4\right)}{99}=-4\)
=> (x+1)+(x+2)+(x+3)+(x+4)=-4.99=-396
=>4x+10=-396
4x=-406
x=-406:4=-101,5
![](https://rs.olm.vn/images/avt/0.png?1311)
(x+1)+(x+2)+(x+3)+........+(x+99)=X+1+X+2+X+3+X+4+...+X+98+X+99=(X+X+X+...+X+X)+(1+2+3+4+...+98+99)
(CÓ 99 SỐ X )
= 99X+4950
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(1-\dfrac{1}{2}\right)\times\left(1-\dfrac{1}{3}\right)\times\left(1-\dfrac{1}{4}\right)\times...\times\left(1-\dfrac{1}{99}\right)\times\left(1-\dfrac{1}{100}\right)\)
\(=\dfrac{1}{2}\times\dfrac{2}{3}\times\dfrac{3}{4}\times...\times\dfrac{98}{99}\times\dfrac{99}{100}\)
\(=\dfrac{1\times2\times3\times...\times98\times99}{2\times3\times4\times...\times99\times100}=\dfrac{1}{100}\)
(1 - 1/2) × (1 - 1/3) × (1 - 1/4) × ... × (1 - 1/99) × (1 - 1/100)
= 1/2 × 2/3 × 3/4 × ... × 98/99 × 99/100
= 1/100
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(1-\dfrac{1}{3}\right)\times\left(1-\dfrac{1}{4}\right)\times\left(1-\dfrac{1}{5}\right)\times\left(1-\dfrac{1}{6}\right)\times\dots\times\left(1-\dfrac{1}{99}\right)\times\left(1-\dfrac{1}{100}\right)\) (sửa đề)
\(=\dfrac{2}{3}\times\dfrac{3}{4}\times\dfrac{4}{5}\times\dfrac{5}{6}\times\dots\times\dfrac{98}{99}\times\dfrac{99}{100}\)
\(=\dfrac{2\times3\times4\times5\times\dots\times98\times99}{3\times4\times5\times6\times\dots\times99\times100}\)
\(=\dfrac{2}{100}\)
\(=\dfrac{1}{50}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
(1+1/2)x(1+1/3)x(1+1/4)x....x(1+1/98)x(1+1/99)
=3/2x4/3x5/4x..........x99/98x100/99
=(3x4x5x........x99x100)/2x3x4x........x98x99
Giản ước ta được:
=100/2
=50
![](https://rs.olm.vn/images/avt/0.png?1311)
(1+1/2)(1+1/3)...(1+1/99)
=(3/2)(4/3)(5/4)...(100/99)
=100/2=50
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{99.100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
Dấu chấm là nhân
a) \(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{99.100}\) \(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{99}-\frac{1}{100}=1-\frac{1}{100}=\frac{99}{100}\)
b) \(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{97.99}\) \(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{97}-\frac{1}{99}=1-\frac{1}{99}=\frac{98}{99}\)
c) Đặt \(C=\frac{4}{5.7}+\frac{4}{7.9}+....+\frac{4}{59.61}\)
\(\Rightarrow\frac{1}{2}C=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+....+\frac{1}{59}-\frac{1}{61}\)
\(\Rightarrow\frac{1}{2}C=\frac{1}{5}-\frac{1}{61}=\frac{56}{305}\)
\(\Rightarrow C=\frac{56}{305}:\frac{1}{2}=\frac{112}{305}\)
CHÚC BẠN HỌC TỐT NHA! ĐÚNG THÌ NHA!
\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right)....\left(1-\frac{1}{99}\right)\)
\(=\frac{1}{2}.\frac{2}{3}....\frac{98}{99}=\frac{1.2....98}{2.3...99}=\frac{1}{99}\)