C = \(\dfrac{5}{2x4}\)+\(\dfrac{5}{4x6}\)+\(\dfrac{5}{6x8}\)+.........+\(\dfrac{5}{48x50}\)
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NB
1
3 tháng 4 2018
Đặt \(A=\frac{5}{4.6}+\frac{5}{6.8}+.....+\frac{5}{48.50}\)
\(\Leftrightarrow\frac{5}{2}A=\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+.....+\frac{2}{48.50}\)
\(\Leftrightarrow\frac{5}{2}A=\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+....+\frac{1}{48}-\frac{1}{50}\)
\(\Leftrightarrow\frac{5}{2}A=\frac{1}{4}-\frac{1}{50}\)
\(\Leftrightarrow\frac{5}{2}A=\frac{23}{100}\Rightarrow A=\frac{23}{100}.\frac{2}{5}=\frac{23}{250}\)
BM
2
W
4 tháng 3 2018
S = 2*4+4*6+6*8+...+46*48+48*50
S6 = 2*4*6+4*6*6+6*8*6+........................+46*48*6+48*50*6
S6=2*4*(6-0)+4*6*(8-2)+6*8*(10-4)+.................................+46*48*(50-44)+48*50*(52-46)
S6 = 2*4*6+4*6*8-2*4*6+6*8*10-4*6*8+..........................................+46*48*50-44*46*48+48*50*52-46*48*50
S6 = 48*50*52=124800
S=124800/6=20800
4 tháng 3 2018
\(S=2\cdot4+4\cdot6+...+48\cdot50\)
\(S=2\left(1\cdot2+2\cdot3+...+24\cdot25\right)\)
\(\Rightarrow3S=2\left(1\cdot2\left(3-0\right)+2\cdot3\left(4-1\right)+...+24\cdot25\left(26-23\right)\right)\)
\(\Rightarrow3S=2\left(1\cdot2\cdot3-0\cdot1\cdot2+2\cdot3\cdot4-1\cdot2\cdot3+...+24\cdot25\cdot26-23\cdot24\cdot25\right)\)
\(\Rightarrow3S=2\cdot24\cdot25\cdot26\)
\(\Rightarrow S=2\cdot8\cdot25\cdot26=10400\)
\(\Rightarrow6S=10400\cdot6=62400\)
21 tháng 10 2021
\(B=\dfrac{1}{2\cdot4}+\dfrac{1}{4\cdot6}+...+\dfrac{1}{46\cdot48}\)
\(=\dfrac{1}{2}\left(\dfrac{2}{2\cdot4}+\dfrac{2}{4\cdot6}+...+\dfrac{2}{46\cdot48}\right)\)
\(=\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{48}\right)\)
\(=\dfrac{1}{2}\cdot\dfrac{23}{48}=\dfrac{23}{96}< \dfrac{1}{4}\)
11 tháng 6 2020
\(\frac{5}{2\cdot4}+\frac{5}{4\cdot6}+\frac{5}{6\cdot8}+.....+\frac{5}{48\cdot60}\)
\(=\frac{5}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+.....+\frac{1}{48}-\frac{1}{50}\right)\)
\(=\frac{5}{2}\left(\frac{1}{2}-\frac{1}{50}\right)\)
Tự tính nốt :p
21 tháng 10 2021
\(A=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{49\cdot50}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{49}-\dfrac{1}{50}\)
\(=\dfrac{49}{50}< 1\)
8 tháng 3 2023
\(=\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}+\dfrac{1}{6}-\dfrac{1}{6}-\dfrac{1}{8}+\dfrac{1}{8}+\dfrac{1}{10}-\dfrac{1}{10}-\dfrac{1}{12}+\dfrac{1}{12}+\dfrac{1}{13}\)
=1/2+1/13
=15/26
DL
3
16 tháng 8 2015
A=5/2x(2/2x4+2/4x6+2/6x8+...+2/14x16)
=5/2x(1/2-1/4+1/4-1/6+...+1/14-1/16)
=5/2x(1/2-1/16)
=5/2x(7/16)
=35/32
29 tháng 3 2016
Giải
1/2x4+1/4x6+1/6x8+...+1/96x98+1/98x100
= 1/2 x (1/2 - 1/4 + 1/4 - 1/6 + 1/6-1/8 + ... + 1/98 - 1/100)
= 1/2 x (1/2 - 1/100)
= 1/2 x 98/100
= 98/200
ĐS: 98/200
LG
1
\(C=\dfrac{5}{2.4}+\dfrac{5}{4.6}+\dfrac{5}{6.8}+...+\dfrac{5}{48.50}\)
Đặt \(C=\dfrac{5}{2}.\left(\dfrac{1}{2.4}+\dfrac{1}{4.6}+\dfrac{1}{6.8}+...+\dfrac{1}{48.50}\right)\)
\(C=\dfrac{5}{2}.\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{48}-\dfrac{1}{50}\right)\)
\(C=\dfrac{5}{2}.\left(\dfrac{1}{2}-\dfrac{1}{50}\right)\)
\(C=\dfrac{5}{2}.\left(\dfrac{25}{50}-\dfrac{1}{50}\right)\)
\(C=\dfrac{5}{2}.\dfrac{24}{50}\)
\(C=\dfrac{12}{10}=\dfrac{6}{5}\)
Vậy \(C=\dfrac{6}{5}\)