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W
4 tháng 8 2018
\(\frac{5}{2.4}+\frac{5}{4.6}+...+\frac{5}{98.100}\)
= \(\frac{5}{2}-\frac{5}{4}+\frac{5}{4}-\frac{5}{6}+...+\frac{5}{98}-\frac{5}{100}\)
= \(\frac{5}{2}-\frac{5}{100}\)
= \(\frac{49}{50}\)
4 tháng 8 2018
\(Q=\frac{5}{2.4}+\frac{5}{4.6}+...+\frac{5}{98.100}\)
\(=5\left(\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{98.100}\right)\)
\(=\frac{5}{2}.2.\left(\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{98.100}\right)\)
\(=\frac{5}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{98.100}\right)\)
\(=\frac{5}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{100}\right)\)
\(=\frac{5}{2}.\left(\frac{1}{2}-\frac{1}{100}\right)=\frac{5}{2}.\frac{49}{100}=\frac{49}{40}\)
\(\Rightarrow Q=\frac{49}{40}\)
CR
3
28 tháng 3 2019
\(A=\frac{-1}{2.4}+\frac{-1}{4.6}+\frac{-1}{6.8}+...+\frac{-1}{98.100}\Leftrightarrow.\)\(-2A=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{98.100}\Leftrightarrow.\)
\(-2A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{97}-\frac{1}{98}+\frac{1}{98}-\frac{1}{100}\Leftrightarrow.\)
\(-2A=\frac{1}{2}-\frac{1}{100}\Leftrightarrow-2A=\frac{49}{100}\Leftrightarrow A=\frac{-49}{200}.\)
ĐÁP SỐ : \(A=\frac{-49}{200}.\)
N
27 tháng 6 2018
\(D=\dfrac{3}{2.4}+\dfrac{3}{4.6}+\dfrac{3}{6.8}+...+\dfrac{3}{98.100}\)
\(=\dfrac{3}{2}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{98}-\dfrac{1}{100}\right)\)
\(=\dfrac{3}{2}\left(\dfrac{1}{2}-\dfrac{1}{100}\right)\)
\(=\dfrac{3}{2}.\dfrac{49}{100}=\dfrac{147}{200}\)
27 tháng 6 2018
\(D=\dfrac{3}{2\cdot4}+\dfrac{3}{4\cdot6}+\dfrac{3}{6\cdot8}+...+\dfrac{3}{98\cdot100}\\ =\dfrac{3}{2}\cdot\left(\dfrac{2}{2\cdot4}+\dfrac{2}{4\cdot6}+\dfrac{2}{6\cdot8}+...+\dfrac{2}{98\cdot100}\right)\\ =\dfrac{3}{2}\cdot\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{98}-\dfrac{1}{100}\right)\\ =\dfrac{3}{2}\cdot\left(\dfrac{1}{2}-\dfrac{1}{100}\right)\\ =\dfrac{3}{2}\cdot\dfrac{49}{100}\\ =\dfrac{147}{200}\)
6 tháng 3 2016
\(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...........+\frac{1}{98.100}\)
\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\)
\(=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)
cho mình nha!
TP
14 tháng 8 2017
Ta có:
\(A=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{98.100}\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{2}{2.4}+\frac{1}{4,6}+\frac{1}{6.8}+...+\frac{1}{98.100}\right)\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\right)\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{100}\right)\)
\(\Rightarrow A=\frac{1}{2}.\frac{49}{100}=\frac{49}{200}\)
T
14 tháng 8 2017
Đặt \(A=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{98.100}\)
\(4-2=2;6-4=2;...\)
\(2A=\frac{1}{2}-\left(\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\right)\)
\(2A=\frac{1}{2}-\frac{1}{100}\)
\(2A=\frac{49}{100}\)
19 tháng 6 2019
\(\frac{1.4}{4.6}+\frac{2.5}{6.8}+...+\frac{48.51}{98.100}\)
=> \(\frac{1}{4}.\left(\frac{1.4}{2.3}+\frac{2.5}{3.4}+...+\frac{48.52}{49.50}\right)\)
=> \(\frac{1}{4}.\left(\frac{2.3-2}{2.3}+\frac{3.4-2}{3.4}+...+\frac{49.50-2}{49.50}\right)\)
=> \(\frac{1}{4}.\left(1-\frac{2}{2.3}+1-\frac{2}{3.4}+...+1-\frac{2}{49.50}\right)\)
=> \(\frac{1}{4}.\left[48-2.\left(\frac{1}{2.3}-\frac{1}{3.4}-\frac{1}{49.50}\right)\right]\)
=> \(\frac{1}{4}.\left[48-2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\right)\right]\)
=> \(\frac{1}{4}.\left[48-2.\left(\frac{1}{2}-\frac{1}{50}\right)\right]\)
=> \(\frac{1}{4}.\left[48-2.\frac{12}{25}\right]\)
=> \(\frac{1}{4}.\frac{1176}{25}=\frac{249}{25}\)
NT
1
10 tháng 9 2016
B=1.3+2.4+3.5+...+97.99+98.100
B=1(2+1)+2(3+1)+....+97(98+1)+98(99+1)
B=1.2+1+2.3+2+....+97.98+97+98.99+98
B=(1.2+2.3+3.4+....+97.98+98.99)+(1+2+3+...+98)
B=98.99.100/3 + 98.99/2
B=323400+4851=328251
6A = 2 . 4 . 6 + 4.6.6 + 6.8.6 + ... + 98 . 100 . 6 = 2.4.6 + 4.6.(8-2) + ... + 98. 100 . (102 - 96)
= 2.4.6 +4.6.8 - 2.4.6 + .... + 98.100 . 102 - 96.98.100
= 98. 100 . 102
= 999600
Suy ra A = 166600
Vậy ______________________
=166600