Question

cho A=1/151+1/152+...+1/200 . so sánh A va 1/4

Answer 1

\(A=\frac{1}{151}+\frac{1}{152}+...+\frac{1}{200}>\frac{1}{200}+\frac{1}{200}+...+\frac{1}{200}=\frac{50}{200}=\frac{1}{4}\)

\(\Rightarrow A>\frac{1}{4}\)

đúng thì cho mik nha

Answer 2

\(A=\frac{1}{151}+\frac{1}{152}+...+\frac{1}{200}\) ( gồm 50 số hạng )

Ta thấy : \(\frac{1}{151}>\frac{1}{152}>...>\frac{1}{200}\)

\(\Rightarrow\frac{1}{151}+\frac{1}{152}+...+\frac{1}{200}>\frac{1}{200}+\frac{1}{200}+...+\frac{1}{200}\) ( gồm 50 số hạng \(\frac{1}{200}\))

\(\Rightarrow\frac{1}{151}+\frac{1}{152}+...+\frac{1}{200}>\frac{1}{200}.50\)

\(\Rightarrow\frac{1}{151}+\frac{1}{152}+...+\frac{1}{200}>\frac{50}{200}\)

\(\Rightarrow\frac{1}{151}+\frac{1}{152}+...+\frac{1}{200}>\frac{1}{4}\)

Hay \(A>\frac{1}{4}\)

Vậy \(A>\frac{1}{4}\)

_HT_