Question

cho B = 1/41 + 1/42 + 1/43 +...+1/60 Chung minh B < 1/2

 

 

Answer 1

ta thấy \(\frac{1}{41}< \frac{1}{40};\frac{1}{42}< \frac{1}{40};\frac{1}{43}< \frac{1}{40};...;\frac{1}{60}< \frac{1}{40}\)

\(\Rightarrow\frac{1}{41}+\frac{1}{42}+\frac{1}{43}+...+\frac{1}{60}< \frac{1}{40}+\frac{1}{40}+\frac{1}{40}+...+\frac{1}{40}=\frac{1}{40}.20=\frac{20}{40}=\frac{1}{2}\)

\(\Rightarrow B< \frac{1}{2}\)( đpcm )

Answer 2

Ta co

1/41<1/40

1/42<1/40

1/43<1/40

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1/60<1/40

\(\Rightarrow\frac{1}{41}+\frac{1}{42}+....+\frac{1}{60}< \frac{1}{40}+\frac{1}{40}+...+\frac{1}{40}=\frac{20}{40}=\frac{1}{2}\)

\(\Rightarrow B< \frac{1}{2}\)