Question

 

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!!

Answer 1

\(P=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}+\frac{15}{4.43}+\frac{13}{43.8}\)

\(\Leftrightarrow\)\(\frac{1}{7}P=\frac{1}{7}\left(\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}+\frac{15}{4.43}+\frac{13}{43.8}\right)\)

                   \(=\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}+\frac{15}{28.43}+\frac{13}{43.56}\)

                   \(=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}+\frac{1}{28}-\frac{1}{43}+\frac{1}{43}-\frac{1}{56}\)

                    \(=\frac{1}{2}-\frac{1}{56}=\frac{27}{56}\)

\(\Leftrightarrow\)\(P=\frac{27}{56}:\frac{1}{7}=3\frac{3}{8}\)\(>3\)  (ĐPCM)

   

Answer 2

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

Answer 3

P=(5/2+4/11+3/22)+1/2.15+13/15.4+15/4.43+13/43.8

P=3+1/2.15+13/15.4+15/4.43+13/43.8

=>P>3