Question

Cho M = 1/50 + 1/51 + ... + 1/98 + 1/99 . So sánh M với 1/2

Answer 1

Ta có :

\(\frac{1}{50}>\frac{1}{100}\)

\(\frac{1}{51}>\frac{1}{100}\)

............

\(\frac{1}{98}>\frac{1}{100}\)

\(\frac{1}{99}>\frac{1}{100}\)

\(\Rightarrow\frac{1}{50}+\frac{1}{51}+....+\frac{1}{98}+\frac{1}{99}>\frac{1}{100}+\frac{1}{100}+....+\frac{1}{100}=\frac{50.1}{100}=\frac{1}{2}\)

\(\Rightarrow M>\frac{1}{2}\)

Answer 2

Ta có: \(\frac{1}{50}>\frac{1}{51}>....>\frac{1}{99}\)

\(\Rightarrow M>\frac{1}{99}+\frac{1}{99}+...+\frac{1}{99}=\frac{50}{99}>\frac{50}{100}=\frac{1}{2}\)

 Vậy M > 1/2

Answer 3

Ta có :

M = \(\frac{1}{50}+\frac{1}{51}+...+\frac{1}{98}+\frac{1}{99}\)

M > \(\frac{1}{100}+\frac{1}{100}+...+\frac{1}{100}+\frac{1}{100}\)( 50 số hạng )

\(=\frac{1}{100}.50=\frac{1}{2}\)

Vậy M > \(\frac{1}{2}\)