\dfrac{1}{9}+\dfrac{1}{10}< \dfrac{1}{8}+\dfrac{1}{8}=\dfrac{1}{4}

\(\frac{1}{5}+\frac{1}{9}+\frac{1}{10}+\frac{1}{41}+\frac{1}{42}\)

\(< \frac{1}{5}+\frac{1}{8}+\frac{1}{8}+\frac{1}{40}+\frac{1}{40}\)

\(=\frac{1}{5}+\frac{1}{4}+\frac{1}{20}=\frac{1}{2}\)

S<1/2 nha bạn

S = \(\frac{1}{5}+\frac{1}{9}+\frac{1}{10}+\frac{1}{41}+\frac{1}{42}=\frac{5932}{12915}=0.459310878\approx0.45\)

\(\frac{1}{2}=0.5\)

Vì 0.45 < 0.5

\(\Leftrightarrow\) S < 1/2

S<1/2 nha bạn

  mình nha

Nhận xét: \(\frac{1}{5}< \frac{1}{42};\frac{1}{9}< \frac{1}{42};\frac{1}{10}< \frac{1}{42};\frac{1}{40}< \frac{1}{42}\)

\(\Rightarrow S< \frac{1}{42}+\frac{1}{42}+\frac{1}{42}+\frac{1}{42}+\frac{1}{42}\)

\(\Rightarrow S< \frac{5}{42}< \frac{21}{42}=\frac{1}{2}\)

Vậy S < 1/2

ta có: S=1159/2520 =>S<1/2

1/5+1/9+1/10+1/40+1/42=1159/2520

                      1159/2520=0.4599.....                  

                                1/2=0.5

Mà:0.5>0.4599

Nên:1/5+1/9+1/10+1/40+1/42>1/2

\(2B=\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+..+\frac{2}{37\cdot38\cdot39}\)

\(2B=\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+..+\frac{1}{37\cdot38}-\frac{1}{38\cdot39}\)

\(2B=\frac{1}{2}-\frac{1}{1482}\)

\(B=\frac{185}{741}\)

\(A>\frac{1}{80}+\frac{1}{80}+..+\frac{1}{80}\)

\(A>\frac{1}{80}\cdot40>\frac{7}{42}\)

\(A>\frac{7}{42}\)