Tính nhanh: \(\frac{1}{4}+\frac{1}{12}+\frac{1}{24}+.....+\frac{1}{924}\)
b. \(\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)
K
Khách
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9 tháng 3 2017
\(B=\dfrac{5}{2.1}+\dfrac{4}{1.11}+\dfrac{3}{11.2}+\dfrac{1}{2.15}+\dfrac{13}{15.4}\)
\(\dfrac{B}{7}=\dfrac{5}{2.7}+\dfrac{4}{7.11}+\dfrac{3}{11.14}+\dfrac{1}{14.15}+\dfrac{13}{15.4}\)
\(\dfrac{B}{7}=\dfrac{1}{2}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{7}{11}+...+\dfrac{1}{15}-\dfrac{1}{28}\)
\(\dfrac{B}{7}=\dfrac{1}{2}-\dfrac{1}{28}\)
\(\dfrac{B}{7}=\dfrac{13}{28}\)
\(B=\dfrac{13}{28}.7=\dfrac{13}{4}\)
PM
2
15 tháng 2 2017
\(B=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)
\(\Rightarrow\frac{B}{7}=\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\)
\(\Rightarrow\frac{B}{7}=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}\)
\(\Rightarrow\frac{B}{7}=\frac{1}{2}-\frac{1}{28}\)
\(\Rightarrow\frac{B}{7}=\frac{14}{28}-\frac{1}{28}\)
\(\Rightarrow\frac{B}{7}=\frac{13}{28}\)
\(\Rightarrow B=\frac{13}{28}.7\)
\(\Rightarrow B=\frac{13}{4}\)
PV
1
LL
18 tháng 5 2018
Trả lời:
\(\frac{5}{2\cdot1}+\frac{4}{1\cdot11}+\frac{3}{11\cdot2}+\frac{1}{2\cdot15}\)\(+\frac{13}{15\cdot4}\)
\(=\frac{5}{2}+\frac{4}{11}+\frac{3}{22}+\frac{1}{30}\)\(+\frac{13}{60}\)
\(=\frac{55+8+3}{22}\)\(+\frac{2+13}{60}\)
\(=\frac{66}{22}\)\(+\frac{1}{4}\)
\(=\frac{13}{4}\)
Hc tốt #
ND
0
TT
0
SK
0
17 tháng 5 2015
\(\Rightarrow\frac{B}{7}=\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\)
\(=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}\)
\(=\frac{1}{2}-\frac{1}{28}=\frac{13}{28}\)
\(\Rightarrow B=\frac{13}{28}.7=\frac{13}{4}\)
HI
2
A= 5/2.1 + 4/1.11 + 3/11.2 + 1/2.15 + 13/5.4
A/7 = 5/2.7 + 4/7.11 + 3/11.13 + 1/14.17 + 13/ 17.20
A/7= 1/2 - 1/7 +1/7 - 1/11 + 1/11 -1/13 + 1/14 - 1/17 + 1/17- 1/20
A/7= 1/2-1/20
A/7= 9/20
A= 9/20 .7
A= 63/20