Cho P=\(\frac{5}{2.1}\)+\(\frac{4}{1.11}\)+\(\frac{3}{11.2}\)+\(\frac{1}{2.15}\)+\(\frac{13}{15.4}\)+\(\frac{15}{4.43}\)+\(\frac{13}{43.8}\)
Chứng tỏ rằng P > 3
Mong mọi người giúp mình !!!
Nhanh nhé!!
K
Khách
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Những câu hỏi liên quan
2 tháng 5 2019
Em nhân từng phân số với \(\frac{1}{7}\)
\(\frac{1}{7}P=\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}+\frac{15}{28.43}+\frac{13}{43.56}\)
\(\frac{1}{7}P=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{43}-\frac{1}{56}\)
\(\frac{1}{7}P=\frac{1}{2}-\frac{1}{56}\)
\(\frac{1}{7}P=\frac{27}{56}\)
\(P=\frac{27}{56}:\frac{1}{7}\)
\(P=\frac{27}{8}>3\)
Vậy P >3
( ko hiểu chỗ nào thì hỏi nhá )
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
9 tháng 3 2017
\(B=\dfrac{5}{2.1}+\dfrac{4}{1.11}+\dfrac{3}{11.2}+\dfrac{1}{2.15}+\dfrac{13}{15.4}\)
\(\dfrac{B}{7}=\dfrac{5}{2.7}+\dfrac{4}{7.11}+\dfrac{3}{11.14}+\dfrac{1}{14.15}+\dfrac{13}{15.4}\)
\(\dfrac{B}{7}=\dfrac{1}{2}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{7}{11}+...+\dfrac{1}{15}-\dfrac{1}{28}\)
\(\dfrac{B}{7}=\dfrac{1}{2}-\dfrac{1}{28}\)
\(\dfrac{B}{7}=\dfrac{13}{28}\)
\(B=\dfrac{13}{28}.7=\dfrac{13}{4}\)
TB
2
29 tháng 7 2017
\(B=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{2}{2.15}+\frac{13}{15.4}\)
\(B=\frac{1}{2}-1+1-\frac{1}{11}+\frac{1}{11}-\frac{1}{2}+\frac{1}{2}-\frac{1}{15}+\frac{1}{15}-\frac{1}{4}\)
\(B=\frac{1}{2}-\frac{1}{4}\)
\(B=\frac{1}{4}\)
HI
2
TT
0
SK
0
\(P=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}+\frac{15}{4.43}+\frac{13}{43.8}\)
\(\Leftrightarrow\)\(\frac{1}{7}P=\frac{1}{7}\left(\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}+\frac{15}{4.43}+\frac{13}{43.8}\right)\)
\(=\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}+\frac{15}{28.43}+\frac{13}{43.56}\)
\(=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}+\frac{1}{28}-\frac{1}{43}+\frac{1}{43}-\frac{1}{56}\)
\(=\frac{1}{2}-\frac{1}{56}=\frac{27}{56}\)
\(\Leftrightarrow\)\(P=\frac{27}{56}:\frac{1}{7}=3\frac{3}{8}\)\(>3\) (ĐPCM)
1/7p= 5/2.7+4/7.11+...+13/43.56
1/7p=1/2-1/7+1/7-1/11+...+1/43-1/56
1/7p=1/2-1/56
1/7p=27/56
suy ra p=27/56.7
p=189/56>3 suy ra đéo phải chứng minh