Question

Cho A  = 1/ 101 + 1/ 102 + 1/103+...+ 1/ 200

Chứng minh rằng : A > 7/ 12

 

 

 

Answer 1

tớ bít nè

Answer 2

A>1/150+1/150+1/150+...+1/150(50 số 1/150)+1/200+1/200+1/20+...+1/200(50 số 1/200).

=>A>1/150*50+1/200*50.

=>A>1/3+1/4=7/12.

Vậy A>7/12(đpcm).

tk mk nha nay mk học bài này,chắc chắn.

-chúc ai tk mk học giỏi-

Answer 3

Ta có :

\(A=\frac{1}{101}+\frac{1}{102}+\frac{1}{103}+...+\frac{1}{200}\)

\(A>\left(\frac{1}{150}+\frac{1}{150}+...+\frac{1}{150}\right)+\left(\frac{1}{200}+\frac{1}{200}+...+\frac{1}{200}\right)\)

\(=\frac{1}{150}.50+\frac{1}{200}.50=\left(\frac{1}{150}+\frac{1}{200}\right).50=\frac{7}{600}.50=\frac{7}{12}\)

\(\Rightarrow A>\frac{7}{12}\)