B=\(\frac{1}{2\cdot4}+\frac{1}{4\cdot6}+\frac{1}{6\cdot8}+...+\frac{1}{96\cdot98}+\frac{1}{98\cdot100}\)
Please help me!!!!!!!!
K
Khách
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A
5
NT
4
2 tháng 4 2018
\(\frac{3}{2.4}+\frac{3}{4.6}+....+\frac{3}{98.100}\)
\(=\frac{3}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{98.100}\right)\)
\(=\frac{3}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+....+\frac{1}{98}-\frac{1}{100}\right)\)
\(=\frac{3}{2}.\left(\frac{1}{2}-\frac{1}{100}\right)\)
\(=\frac{3}{2}.\frac{49}{100}=\frac{147}{200}\)
KT
2 tháng 4 2018
\(\frac{3}{2.4}+\frac{3}{4.6}+\frac{3}{6.8}+...+\frac{3}{98.100}\)
\(=\frac{3}{2}\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+....+\frac{2}{98.100}\right)\)
\(=\frac{3}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+....+\frac{1}{98}-\frac{1}{100}\right)\)
\(=\frac{3}{2}\left(\frac{1}{2}-\frac{1}{100}\right)\)
\(=\frac{3}{2}.\frac{49}{100}=\frac{147}{200}\)
VA
25 tháng 7 2016
Đặt \(A=\frac{5}{2.4}+\frac{5}{4.6}+\frac{5}{6.8}+..+\frac{5}{100.102}\)
\(\frac{2}{5}A=\frac{2}{2.4}+\frac{2}{4.6}+\frac{3}{6.8}+...+\frac{2}{100.102}\)
\(\frac{2}{5}A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{100}-\frac{1}{102}\)
\(\frac{2}{5}A=\frac{1}{2}-\frac{1}{102}\)
\(A=\frac{25}{51}:\frac{2}{5}\)
\(A=\frac{125}{102}\)
Ủng hộ mk nha !!! *_*
S
26 tháng 7 2016
\(\text{Đ}\text{ặt}:A=\frac{5}{2.4}+\frac{5}{4.6}+\frac{5}{6.8}+..+\frac{5}{100.102}\)
\(\frac{2}{5}A=\frac{2}{2.4}+\frac{2}{4.6}+\frac{3}{6.8}+...+\frac{2}{100.102}\)
\(\frac{2}{5}A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{100}-\frac{1}{102}\)
\(\frac{2}{5}A=\frac{1}{2}-\frac{1}{102}\)
\(A=\frac{25}{51}:\frac{2}{5}\)
\(A=\frac{125}{102}\)
HT
23 tháng 9 2015
\(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{99.100}\)
= \(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{99}-\frac{1}{100}\)
= \(\frac{1}{3}-\frac{1}{100}\)
= \(\frac{97}{300}\)
DP
14 tháng 6 2017
\(E=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+....+\frac{1}{2016.2018}\)
\(E=\frac{4-2}{2.4}+\frac{6-4}{4.6}+\frac{8-6}{6.8}+...+\frac{2018-2016}{2016.2018}\)
\(2E=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2016}-\frac{1}{2018}\)
\(E=\left(\frac{1}{2}-\frac{1}{2018}\right).\frac{1}{2}\)
\(E=\frac{504}{1009}.\frac{1}{2}\)
\(E=\frac{252}{1009}\)
14 tháng 6 2017
\(E=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2016}-\frac{1}{2018}\)
\(E=\frac{1}{2}-\frac{1}{2018}\)
\(E=\frac{1005}{2018}\)
HT
1
8 tháng 11 2015
Đặt \(D=\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{98.100}\)
=>\(2D=\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{98.100}\)
=>\(2D=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{100}\)
=>\(2D=\frac{1}{2}-\frac{1}{100}\)
=>\(2D=\frac{49}{100}\)
=>\(D=\frac{49}{50}\)
\(B=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{96}-\frac{1}{98}+\frac{1}{98}-\frac{1}{100}\right)\)
\(B=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{100}\right)=\frac{1}{2}.\frac{49}{100}=\frac{49}{200}\)
Bn Nguyễn Tuấn Minh làm đúng rồi đó bạn