Question

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

Chứng minh rằng C>5/8

 

Answer 1

Ta có:

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

\(c=\)(\(\frac{1}{101}\)\(+\)\(\frac{1}{102}\)\(+\)...\(+\)\(\frac{1}{120}\))\(+\)(\(\frac{1}{121}\)\(+\)\(\frac{1}{122}\)\(+\)...\(+\)\(\frac{1}{150}\))\(+\)(\(\frac{1}{151}\)\(+\)\(\frac{1}{152}\)\(+\)...\(+\)\(\frac{1}{180}\))\(+\)(\(\frac{1}{181}\)\(+\)\(\frac{1}{182}\)\(+\)...\(+\)\(\frac{1}{200}\))>20\(.\)\(\frac{1}{120}\)\(+\)30\(.\)\(\frac{1}{150}\)\(+\)30\(.\)\(\frac{1}{180}\)\(+\)20\(.\)\(\frac{1}{200}\)= \(\frac{1}{6}+\frac{1}{5}\)\(+\)\(\frac{2}{6}+\frac{1}{10}\)= \(\frac{19}{30}\)=\(\frac{76}{120}\)> \(\frac{75}{120}\)=\(\frac{5}{8}\)

=>\(c\)>\(\frac{5}{8}\)(đpcm)

_Hok tốt_

Answer 2

Cảm ơn nhiều !