1/4+1/28+1/70+.....+1/550
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DQ
0
LB
0
DD
20 tháng 9 2016
A=5/4+5/28+5/70+5/130+...+5/418+5/550
Xét:5/1.4+5/4.7+5/7.10+5/10.13+...+5/19.22+5/22.25
=5-5/25
=24/5
LN
1
17 tháng 5 2020
\(\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+\frac{3}{130}+....+\frac{3}{418}+\frac{3}{550}\)
\(\Leftrightarrow\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{19.22}+\frac{3}{22.25}\)
\(\Leftrightarrow\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{19}-\frac{1}{22}+\frac{1}{22}-\frac{1}{25}\)
\(\Leftrightarrow\frac{1}{1}-\frac{1}{25}=\frac{24}{25}\)
Nhớ k cho m nhé!
5 tháng 8 2016
Ta có:
1/4 = 1/3( 1-1/4)
1/28 = 1/3( 1/4 - 1/7)
1/70 = 1/3( 1/7 - 1/10)
..............................
1/10300 = 1/3( 1/100 - 1/103)
Cộng vế với vế ta có:
S = 1/4+1/28+1/70+1/130+...+1/10300 = 1/3( 1-1/103)
S = 34/103
19 tháng 4 2020
\(3M=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{97.100}\)
\(3M=\frac{4-1}{1.4}+\frac{7-4}{4.7}+...+\frac{100-97}{97.100}\)
\(3M=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{100}\)
\(3M=1-\frac{1}{100}\)
\(3M=\frac{99}{100}\)
\(M=\frac{33}{100}\)
MV
1
LT
1
Đặt :
\(M=\dfrac{1}{4}+\dfrac{1}{28}+\dfrac{1}{70}+................+\dfrac{1}{550}\)
\(\Rightarrow M=\dfrac{1}{1.4}+\dfrac{1}{4.7}+\dfrac{1}{7.10}+..................+\dfrac{1}{22.25}\)
\(\Rightarrow3M=\dfrac{3}{1.4}+\dfrac{3}{4.7}+.................+\dfrac{3}{22.25}\)
\(\Rightarrow3M=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+.........+\dfrac{1}{22}-\dfrac{1}{25}\)
\(\Rightarrow3M=1-\dfrac{1}{25}\)
\(\Rightarrow3M=\dfrac{24}{25}\)
\(\Rightarrow M=\dfrac{24}{75}\)
Đặt:
\(A=\dfrac{1}{4}+\dfrac{1}{28}+\dfrac{1}{70}+.....+\dfrac{1}{550}\)
\(A=\dfrac{1}{1.4}+\dfrac{1}{4.7}+\dfrac{1}{7.10}+.....+\dfrac{1}{22.25}\)
\(A=\dfrac{1}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+.....+\dfrac{1}{22}-\dfrac{1}{25}\right)\)
\(A=\dfrac{1}{3}\left(1-\dfrac{1}{25}\right)=\dfrac{1}{3}.\dfrac{24}{25}=\dfrac{25}{72}\)