6/1.3.7 + 6/3.7.9 + 6/7.9.13 + 6/9.13.15 + 6/13.15.19
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8 tháng 8 2017
6/1.3.7 + 6/3.7.9 + 6/7.9.13 + 6/9.13.15 + 6/13.15.19
=\frac{6}{8}\left(\frac{8}{1.3.7}+\frac{8}{3.7.9}+...+\frac{8}{13.15.19}\right)=86(1.3.78+3.7.98+...+13.15.198)
=\frac{6}{8}\left(\frac{1}{1.3}-\frac{1}{3.7}+\frac{1}{3.7}-\frac{1}{7.9}+...+\frac{1}{13.15}-\frac{1}{15.19}\right)=86(1.31−3.71+3.71−7.91+...+13.151−15.191)
=\frac{6}{8}\cdot\left(\frac{1}{3}-\frac{1}{285}\right)=86⋅(31−2851)
=\frac{6}{8}\cdot\frac{94}{285}=86⋅28594
=\frac{47}{190}=19047
HM
8 tháng 8 2017
6/1.3.7 + 6/3.7.9 + 6/7.9.13 + 6/9.13.15 + 6/13.15.19
=68(81.3.7+83.7.9+...+813.15.19)=\frac{6}{8}\left(\frac{8}{1.3.7}+\frac{8}{3.7.9}+...+\frac{8}{13.15.19}\right)=86(1.3.78+3.7.98+...+13.15.198)
=68(11.3−13.7+13.7−17.9+...+113.15−115.19)=\frac{6}{8}\left(\frac{1}{1.3}-\frac{1}{3.7}+\frac{1}{3.7}-\frac{1}{7.9}+...+\frac{1}{13.15}-\frac{1}{15.19}\right)=86(1.31−3.71+3.71−7.91+...+13.151−15.191)
=68⋅(13−1285)=\frac{6}{8}\cdot\left(\frac{1}{3}-\frac{1}{285}\right)=86⋅(31−2851)
=68⋅94285=\frac{6}{8}\cdot\frac{94}{285}=86⋅28594
=47190=\frac{47}{190}=19047
HH
29 tháng 6 2018
Giải:
Đặt:
\(A=\dfrac{6}{1.3.7}+\dfrac{6}{3.7.9}+\dfrac{6}{7.9.13}+\dfrac{6}{9.13.15}+\dfrac{6}{13.15.19}\)
\(\Leftrightarrow A=\dfrac{6}{8}\left(\dfrac{8}{1.3.7}+\dfrac{8}{3.7.9}+\dfrac{8}{7.9.13}+\dfrac{8}{9.13.15}+\dfrac{8}{13.15.19}\right)\)
\(\Leftrightarrow A=\dfrac{6}{8}\left(\dfrac{1}{1.3}-\dfrac{1}{3.7}+\dfrac{1}{3.7}-\dfrac{1}{7.9}+\dfrac{1}{7.9}-\dfrac{1}{9.13}+\dfrac{1}{9.13}-\dfrac{1}{13.15}+\dfrac{1}{13.15}-\dfrac{1}{15.19}\right)\)
\(\Leftrightarrow A=\dfrac{6}{8}\left(\dfrac{1}{1.3}-\dfrac{1}{15.19}\right)\)
\(\Leftrightarrow A=\dfrac{6}{8}\left(\dfrac{1}{3}-\dfrac{1}{285}\right)\)
\(\Leftrightarrow A=\dfrac{6}{8}.\dfrac{94}{285}\)
\(\Leftrightarrow A=\dfrac{47}{190}\)
Vậy ...
T
Tính tổng :\(\frac{6}{1.3.5}+\frac{6}{3.7.9}+\frac{6}{7.9.13}+\frac{6}{9.13.15}+\frac{6}{13.15.19}\)
0
LD
1
7 tháng 8 2017
B=6/1.3.5+6/3.7.9+6/7.9.13+6/9.13.15+6/13.15.19
=2/5+2/63+2/273+2/585+2/1235
=886/1995
C
1
17 tháng 7 2017
\(C=\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}+...+\dfrac{2}{399}\)
\(C=\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{19.21}\)
\(C=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{19}-\dfrac{1}{21}\)
\(C=\dfrac{1}{3}-\dfrac{1}{21}\)
\(C=\dfrac{2}{7}\)
6/1.3.7 + 6/3.7.9 + 6/7.9.13 + 6/9.13.15 + 6/13.15.19
\(=\frac{6}{8}\left(\frac{8}{1.3.7}+\frac{8}{3.7.9}+...+\frac{8}{13.15.19}\right)\)
\(=\frac{6}{8}\left(\frac{1}{1.3}-\frac{1}{3.7}+\frac{1}{3.7}-\frac{1}{7.9}+...+\frac{1}{13.15}-\frac{1}{15.19}\right)\)
\(=\frac{6}{8}\cdot\left(\frac{1}{3}-\frac{1}{285}\right)\)
\(=\frac{6}{8}\cdot\frac{94}{285}\)
\(=\frac{47}{190}\)
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