Question

A=1/100+1/101+1/102+1/103+...+1/200.So sanh A voi 3/4

Answer 1

A=\(\frac{1}{100}\)+\(\frac{1}{101}\)+\(\frac{1}{102}\)+...+\(\frac{1}{200}\)

   (Sử dung phương pháp chặn số đầu)

\(\frac{1}{100}\)>\(\frac{1}{101}\)

\(\frac{1}{100}\)>\(\frac{1}{102}\)

           ...

\(\frac{1}{100}\)>\(\frac{1}{200}\)

nên \(\frac{1}{100}\)+\(\frac{1}{101}\)+\(\frac{1}{102}\)+...+\(\frac{1}{200}\)> \(\frac{1}{100}\)+\(\frac{1}{100}\)+...+\(\frac{1}{100}\)(có 101 phân số)

\(\Rightarrow\)\(\frac{1}{100}\)+\(\frac{1}{101}\)+\(\frac{1}{102}\)+...+\(\frac{1}{200}\)>101.\(\frac{1}{100}\)=\(\frac{101}{100}\)>1>\(\frac{3}{4}\)

\(\Rightarrow\)A >\(\frac{3}{4}\)