tinh tong:A=2/1.7+2/7/13+2/13.19+...+2/601.607
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CN
6
16 tháng 4 2016
rất đơn giản
nhân 3 vào tư và mẫu sau đó tách \(\frac{1}{3}\) ra
ta có \(\frac{1}{3}.\left(\frac{6}{1.7}+\frac{6}{7.13}+...+\frac{6}{601.607}\right)\)
=\(\frac{1}{3}.\left(\frac{1}{1}-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+...+\frac{1}{601}-\frac{1}{607}\right)\)
=1/3 . ( 1-1/207)
bây giờ tự tính nha
13 tháng 8 2018
Ta có :\(\left(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+...+\frac{5}{601.607}\right)\)\(\ne0\)
\(\Rightarrow x=0\)
13 tháng 8 2018
\(X:\left(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+......+\frac{5}{601.607}\right)=0\)
\(\Rightarrow X:\left(\frac{5}{1}-\frac{5}{7}+\frac{5}{7}-\frac{5}{13}+\frac{5}{13}+......+\frac{5}{601}-\frac{5}{607}\right)=0\)
\(\Leftrightarrow X:\left(5-\frac{5}{607}\right)=0\)
\(\Leftrightarrow X:\frac{3030}{607}=0\)
\(\Leftrightarrow X=0\)
CÁCH 2:\(X:\left(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+....+\frac{5}{601.607}\right)=0\)
\(\Leftrightarrow X=0.\left(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+....+\frac{5}{601.607}\right)\)
\(\Leftrightarrow X=0\)
S
4 tháng 5 2023
a/\(C=\dfrac{2}{1.7}+\dfrac{2}{7.13}+\dfrac{2}{13.19}+...+\dfrac{2}{1013.1019}\)
\(=\dfrac{1}{3}\left(\dfrac{6}{1.7}+\dfrac{6}{7.13}+\dfrac{6}{13.19}+...+\dfrac{6}{1013.1019}\right)\)
\(=\dfrac{1}{3}\left(1-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{19}+...+\dfrac{1}{1013}-\dfrac{1}{1019}\right)\)
\(=\dfrac{1}{3}\left(1-\dfrac{1}{1019}\right)\)
\(=\dfrac{1}{3}\cdot\dfrac{1018}{1019}\)
\(=\dfrac{1018}{3057}\)
b/\(D=\dfrac{7}{1.9}+\dfrac{7}{9.17}+\dfrac{7}{17.25}+...+\dfrac{7}{2011.2019}\)
\(=\dfrac{7}{8}\left(\dfrac{8}{1.9}+\dfrac{8}{9.17}+\dfrac{8}{17.25}+...+\dfrac{8}{2011.2019}\right)\)
\(=\dfrac{7}{8}\left(1-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{25}+...+\dfrac{1}{2011}-\dfrac{1}{2019}\right)\)
\(=\dfrac{7}{8}\left(1-\dfrac{1}{2019}\right)\)
\(=\dfrac{7}{8}\cdot\dfrac{2018}{2019}\)
\(=\dfrac{7063}{8076}\)
DV
1
WR
15 tháng 6 2015
G=6(6/1.7+6/7.13+6/13.19+..+6/n(n+6) )
=6(1-1/7+1/7-1/13+1/13-1/19+....+1/n-1/n+6)
=6(1-n/n+6)
=6.6/n+6
=36/n+6
vậy G=36/n+6
NN
1 tháng 4 2019
\(\frac{1}{1.7}+\frac{1}{7.13}+\frac{1}{13.19}+...+\frac{1}{61.67}\)
=6.\(\left(\frac{1}{1.7}+\frac{1}{7.13}+...+\frac{1}{61.67}\right)\):6
=\((\frac{6}{1.7}+\frac{6}{7.13}+...+\frac{6}{61.67}):6\)
=\(\left(1-\frac{1}{7}+\frac{1}{7}+\frac{1}{13}+...+\frac{1}{61}+\frac{1}{67}\right):6\)
=\(\left(1-\frac{1}{67}\right):6\)
=\(\frac{66}{67}:6=\frac{66}{67}.\frac{1}{6}=\frac{11}{67}\)
NC
0
22 tháng 7 2017
E = \(\frac{36}{1\cdot7}+\frac{36}{7\cdot13}+...+\frac{36}{94\cdot100}=\frac{36}{6}\left[\frac{1}{1\cdot7}+\frac{1}{7\cdot13}+...+\frac{1}{94\cdot100}\right]\)
\(=6\left[1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+...+\frac{1}{94}-\frac{1}{100}\right]=6\left[1-\frac{1}{100}\right]\)
\(=6\cdot\frac{99}{100}=\frac{297}{50}\)
F = \(\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+...+\frac{1}{\left[3a+2\right]\left[3a+5\right]}\)
\(=\frac{1}{2\cdot5}+\frac{1}{5\cdot8}+\frac{1}{8\cdot11}+...+\frac{1}{\left[3a+2\right]\left[3a+5\right]}\)
\(=\frac{1}{3}\left[\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{3a+2}-\frac{1}{3a+5}\right]\)
\(=\frac{1}{3}\left[\frac{1}{2}-\frac{1}{3a+5}\right]=\frac{1}{6}-\frac{1}{9a+15}\)
G = \(\frac{1}{2\cdot3}+\frac{2}{3\cdot5}+\frac{3}{5\cdot8}+\frac{4}{8\cdot12}+\frac{5}{12\cdot17}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{12}-\frac{1}{17}\)
\(=\frac{1}{2}-\frac{1}{17}=\frac{15}{34}\)