\(B=\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}>\frac{1}{16}+\frac{1}{16}+\frac{1}{16}+...+\frac{1}{16}=\frac{16}{16}=1\)

B = 1/4 + 1/5 + 1/6 + ... + 1/19 > 1

B = 1/4+﴾1/5+1/6+...+1/9﴿+﴾1/10+1/11+...+1/19﴿

Vì 1/5+1/6+...+1/9 > 1/9+1/9+...+1/9 nên 1/5+1/6+...+1/9 > 5/9 >1/2

Vì 1/10+1/11+...+1/19 > 1/19+1/19+...+1/19 nên 1/10+1/11+...+1/19 > 10/19 >1/2

Suy ra: B > 1/4+1/2+1/2 > 1 

Ta xét : \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{19}-\frac{1}{20}=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{19}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{20}\right)\)

\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{20}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+....+\frac{1}{20}\right)\)

\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{20}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{9}+\frac{1}{10}\right)\)

\(=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+....+\frac{1}{20}\)

Vì \(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+....+\frac{1}{20}=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}\)

nên \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{19}-\frac{1}{20}=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+....+\frac{1}{20}\) ( đpcm )

Nhiều cách lắm,ví dụ nhé:
B = ( \(\frac{1}{4}+\frac{1}{5}+...+\frac{1}{11}\) ) + ( \(\frac{1}{12}+\frac{1}{13}+...+\frac{1}{19}\))
        ______________________        _________________________
                      B                                                  C
-Ta xét B ( vì bạn bảo chi tiết nên tôi làm như vậy còn ở bài thì không cần như vậy )
\(\frac{1}{4}>\frac{1}{12}\);...; \(\frac{1}{11}>\frac{1}{12}\)
-Xét C : \(\frac{1}{12}>\frac{1}{20};...;\frac{1}{19}>\frac{1}{20}\)
(=) B > \(\left(\frac{1}{12}+\frac{1}{12}+...+\frac{1}{12}\right)+\left(\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}\right)\)
                  _________________                    ___________________
                      8 số                                               8 số
(=) B > \(\frac{8}{12}+\frac{8}{20}\)= \(\frac{2}{3}+\frac{2}{5}\)= \(\frac{16}{15}\)> 1
(=) B > 1 (đpcm)

\(B=\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}>\frac{1}{4}+\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}=\frac{1}{4}+\frac{15}{20}=1\)

\(B=\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}>\frac{1}{20}+\frac{1}{20}+....+\frac{1}{20}+\frac{1}{4}=\frac{3}{4}+\frac{1}{4}=1\)

Vậy B>1

Hok tốt

B = \(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}\)

B = \(\left(\frac{1}{4}+\frac{1}{5}+...+\frac{1}{11}\right)+\left(\frac{1}{12}+\frac{1}{13}+...+\frac{1}{19}\right)>\left(\frac{1}{11}+...+\frac{1}{11}\right)+\left(\frac{1}{19}+...+\frac{1}{19}\right)\)

B > \(\frac{240}{209}\)

Vậy B > 1.

B=1/4+(1/5+1/6+...+1/19)>1/4+15x1/20

B>1/4+15/20=1/4+3/4=1

\(\Rightarrow\)B>1

help me

zúp mình zới

Nhanh lên nhé

Giups mnihf đi

Mk làm câu a thôi nhé :)

Vì \(\frac{1}{5^2}< \frac{1}{4.5}\)

     \(\frac{1}{6^2}< \frac{1}{5.6}\)

       ...

       \(\frac{1}{100^2}< \frac{1}{99.100}\)

\(=>\frac{1}{5^2}+\frac{1}{6^2}+...+\frac{1}{100^2}\)

\(< \)\(\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{99.100}\)\(=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{99}-\frac{1}{100}\)

                                                                          \(=\frac{1}{4}-\frac{1}{100}\)(1)

Vì \(\frac{1}{5^2}>\frac{1}{5.6}\)

     \(\frac{1}{6^2}>\frac{1}{6.7}\)

       ...

       \(\frac{1}{100^2}>\frac{1}{100.101}\)

\(=>\frac{1}{5^2}+\frac{1}{6^2}+...+\frac{1}{100^2}\)

\(>\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{100.101}=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-...+\frac{1}{100}-\frac{1}{101}\)

                                                                   \(=\frac{1}{5}-\frac{1}{101}\)(2)

Từ (1) và (2) => ĐPCM

\(\frac{1}{4}+\frac{1}{5}+...+\frac{1}{19}=\frac{1}{4}+\left(\frac{1}{5}+...+\frac{1}{9}\right)+\left(\frac{1}{10}+...+\frac{1}{19}\right)\) > \(\frac{1}{4}+\left(\frac{1}{9}+\frac{1}{9}+...+\frac{1}{9}\right)+\left(\frac{1}{19}+...+\frac{1}{19}\right)\)> \(\frac{1}{4}+\frac{5}{9}+\frac{10}{19}>\frac{1}{4}+\frac{1}{2}+\frac{1}{2}=1\)

Vậy \(\frac{1}{4}+\frac{1}{5}+...+\frac{1}{19}>1\)