Tính nhanh
A= 3/4+3/28+3/70+3/130+3/208+3/304
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15 tháng 1 2017
Ta có:
\(\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+\frac{3}{130}+\frac{3}{208}\)
\(=\frac{3}{1\times4}+\frac{3}{4\times7}+\frac{3}{7\times10}+\frac{3}{10\times13}+\frac{3}{13\times16}\)
\(=\frac{4-1}{1\times4}+\frac{7-4}{4\times7}+\frac{10-7}{7\times10}+\frac{13-10}{10\times13}+\frac{16-13}{13\times16}\) \(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}\)
\(=1-\frac{1}{16}\)
\(=\frac{15}{16}\)
Chắc chắn đúng nhé !
DT
Dang Tung
CTVHS
23 tháng 8 2023
\(\dfrac{3}{4}+\dfrac{3}{28}+\dfrac{3}{70}+\dfrac{3}{130}+\dfrac{3}{208}+\dfrac{3}{304}\\ =\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+\dfrac{3}{10.13}+\dfrac{3}{13.16}+\dfrac{3}{16.19}\\ =1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{19}\\ =1-\dfrac{1}{19}=\dfrac{18}{19}\)
TN
23 tháng 8 2023
\(\dfrac{3}{4}+\dfrac{3}{28}+\dfrac{3}{70}+\dfrac{3}{130}+\dfrac{3}{208}+\dfrac{3}{304}\)
\(=\dfrac{3}{1\times4}+\dfrac{3}{4\times7}+\dfrac{3}{7\times10}+\dfrac{3}{10\times13}+\dfrac{3}{13\times16}+\dfrac{3}{16\times19}\)
\(=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{19}\)
\(=1-\dfrac{1}{19}\)
=\(\dfrac{18}{19}\)
23 tháng 3 2020
\(B=\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+\frac{3}{130}+\frac{3}{208}+\frac{3}{304}\)
\(\Rightarrow B=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}+\frac{3}{16.19}\)
\(\Rightarrow B=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}+\frac{1}{16}-\frac{1}{19}\)
\(\Rightarrow B=1-\frac{1}{19}=\frac{18}{19}\)
Vậy \(B=\frac{18}{19}\)
Chúc bn học tốt
24 tháng 3 2020
B = \(\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+\frac{3}{130}+\frac{3}{208}+\frac{3}{304}\)
= \(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}+\frac{3}{16.19}\)
= \(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-...+\frac{1}{13}-\frac{1}{16}\)
= \(1-\frac{1}{16}\)
= \(\frac{15}{16}\)
TM
11 tháng 6 2016
\(C=\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{997.999}\)
\(\Leftrightarrow C=\frac{5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{997.999}\right)\)
\(\Leftrightarrow C=\frac{5}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{997}-\frac{1}{999}\right)\)
\(\Leftrightarrow C=\frac{5}{2}\left(1-\frac{1}{999}\right)=\frac{5}{2}.\frac{998}{999}=\frac{2495}{999}=2\frac{497}{999}\)
\(A=\frac{2}{4}+\frac{2}{28}+\frac{2}{70}+\frac{2}{130}+\frac{2}{208}\)
\(\Leftrightarrow A=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+\frac{2}{10.13}+\frac{2}{13.16}\)
\(\Leftrightarrow A=\frac{2}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}\right)\)
\(\Leftrightarrow A=\frac{2}{3}\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}\right)\)
\(\Leftrightarrow A=\frac{2}{3}\left(1-\frac{1}{16}\right)=\frac{2}{3}.\frac{15}{16}=\frac{5}{8}\)
11 tháng 6 2016
C = 5/1x3 + 5/3x5 + 5/5x7 + ... + 5/997x999
C = 5 - 5/3 + 5/3 - 5/5 + 5/5 - 5/7 + ... + 5/997 - 5/999
C = 5 - 5/999
C = bạn tự tính nhé !
A = 2/4 + 2/28 + 2/70 + 2/130 + 2/208
A = 2/1x4 + 2/4x7 + 2/7x10 + 2/10x13 + 2/13x16
A = 2 - 2/4 + 2/4 - 2/7 + 2/7 - 2/10 + 2/10 - 2/13 + 2/13 - 2/16
A = 2 - 2/16
A = bạn tự tính nhé !
QT
2
10 tháng 3 2020
\(\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+...+\frac{3}{10300}\)
\(=\frac{3}{1\times4}+\frac{3}{4\times7}+\frac{3}{7\times10}+...+\frac{3}{100\times103}\)
\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{100}-\frac{1}{103}\)
\(=1-\frac{1}{103}=\frac{102}{103}\)
10 tháng 9 2017
b) D = \(\frac{3}{4}+\frac{3}{8}+\frac{3}{70}+\frac{3}{130}+\frac{3}{208}+\frac{3}{304}\)
D = \(3\left(\frac{1}{4}+\frac{1}{28}+\frac{1}{70}+\frac{1}{130}+\frac{1}{208}+\frac{1}{304}\right)\)
D = \(3\left(\frac{1}{1x4}+\frac{1}{4x7}+\frac{1}{7x10}+\frac{1}{10x13}+\frac{1}{13x16}+\frac{1}{16x19}\right)\)
D = \(\frac{1}{1}-\frac{1}{19}=\frac{18}{19}\)
Chắc vậy
MH
4
T
9 tháng 9 2018
\(\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+\frac{3}{130}+....+\frac{3}{304}.\)
\(=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+.....+\frac{3}{16.19}\)
\(=\frac{4-1}{1.4}+\frac{7-4}{4.7}+\frac{10-7}{7.10}+\frac{13-10}{10.13}+.....+\frac{19-16}{16.19}\)
\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+....+\frac{1}{16}-\frac{1}{19}\)
\(=1-\frac{1}{19}=\frac{18}{19}\)
9 tháng 9 2018
3/4+3/28+3/70+3/130+...+3/304
= 3 /1.4 + 3/4.7 + 3/7.10 + 3/10.13 +....+ 3 /16.19
= 1 -1/4 + 1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 + ...+1/16 - 1/19
= 1 - 1/19
=18/19
A=\(\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+\frac{3}{130}+\frac{3}{208}+\frac{3}{304}\)
A= \(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}+\frac{3}{16.19}\)
A= \(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}\)
A= 1 - \(\frac{1}{19}\)
A= \(\frac{18}{19}\)
X=3/4+3/28+...+3/304
X=3/1x4+3/4x7+....+3/13x16
X=1-1/4+1/4-1/7+....+1/13-1/16
X=1-1/16
X=15/16
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