Tính:
1. (1 - 1/2) (1 - 1/3) ... (1- 1 / 100)
2. 1 / 2.4 + 1 / 4.6 ... + 1 / 98.100
K
Khách
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Những câu hỏi liên quan
WR
1
17 tháng 6 2015
\(2P=\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{98.100}\)
\(2P=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}+...+\frac{1}{98}-\frac{1}{100}\)
\(2P=\frac{1}{2}-\frac{1}{100}\)
=> P =\(\frac{49}{100}:2=\frac{49}{100}\cdot\frac{1}{2}=\frac{49}{200}\)
NX
0
MH
12 tháng 4 2022
\(x-\dfrac{1}{2}\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+...+\dfrac{2}{98.100}\right)=\dfrac{1}{100}\)
\(x-\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{98}-\dfrac{1}{100}\right)=\dfrac{1}{100}\)
\(x-\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{100}\right)=\dfrac{1}{100}\)
\(x=\dfrac{51}{200}\)
VT
1
NN
Nguyễn Ngọc Anh Minh
CTVHS
VIP
19 tháng 10 2023
\(C=\dfrac{4}{1.3}.\dfrac{9}{2.4}.\dfrac{16}{3.5}.\dfrac{25}{4.6}....\dfrac{9801}{9800}=\)
\(=\dfrac{2^2.3^2.4^2.5^2.....99^2}{1.2.3^2.4^2.5^2....98^2.99.100}=\dfrac{2.99}{100}=\dfrac{198}{100}=1,98\)
NA
0
TT
1
3 tháng 8 2015
=1-1/3-1/2+1/4+1/3-1/5-1/4+1/6+...+1/97-1/99-1/98+1/100
=1-1/2-1/99-1/98=2327/4851
TT
4
EC
11 tháng 8 2016
\(\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{98.100}\)
\(=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{100}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{100}\right)\)
\(=\frac{1}{2}.\frac{49}{100}\)
\(=\frac{49}{200}\)
Tính:
1. \(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)...\left(1-\dfrac{1}{100}\right)\)
\(=\left(\dfrac{2}{2}-\dfrac{1}{2}\right)\left(\dfrac{3}{3}-\dfrac{1}{3}\right)...\left(\dfrac{100}{100}-\dfrac{1}{100}\right)\)
\(=\dfrac{1}{2}.\dfrac{2}{3}...\dfrac{99}{100}\)
\(=\dfrac{1}{100}\)
\(\Rightarrow\dfrac{1}{100}\)
2. \(\dfrac{1}{2.4}+\dfrac{1}{4.6}+...+\dfrac{1}{98.100}\)
\(=\dfrac{1}{2}.\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{98}-\dfrac{1}{100}\right)\)
\(=\dfrac{1}{2}.\left(\dfrac{1}{2}-\dfrac{1}{100}\right)\)
\(=\dfrac{1}{2}.\left(\dfrac{50}{100}-\dfrac{1}{100}\right)\)
\(=\dfrac{1}{2}.\dfrac{49}{100}\)
\(=\dfrac{49}{200}\)
\(\Rightarrow\dfrac{49}{200}\)