1/7 + 1/12 + 1/25 + 1/49 + 1/97 < 1/3

1/7 + 1/12 + 1/25 + 1/49 + 1/97 < 1/3

Ta có : 1/7 + 1/13 + 1/25 + 1/47 + 1/97 < 1/6 + 1/12 + 1/24 + 1/46 + 1/96

1/7 + 1/13 + 1/25 + 1/47 + 1/97 < 1/6 + 1/6.2 + 1/6.4 + 1/6.8 + 1/6.16

1/7 + 1/13 + 1/25 + 1/47 + 1/97 < 1 + ( 1/2 + 1/4 + 1/8 + 1/16 )

1/7 + 1/13 + 1/25 + 1/47 + 1/97 < 1/6 x ( \(\frac{16+8+4+2+1}{16}\) )

1/7 + 1/13 + 1/25 + 1/47 + 1/97 < 16 x 31/16

1/7 + 1/13 + 1/25 + 1/47 + 1/97 < 31/96 + 31/93

Mà : 91/93 = 1/3

Nên 1/7 + 1/13 + 1/25 + 1/47 + 1/97 < 1/3

1/7 + 1/13 + 1/25 + 1/19 + 1/97 <1

tk vì lười =))

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\(A=\frac{14}{98}+\frac{7}{91}+\frac{4}{100}+\frac{2}{98}+\frac{1}{97}

Ta có : 1/7 + 1/13 +1/25 + 1/47 + 1/97 < 1/6 + 1/12 + 1/24 + 1/48 + 1/96

1/7 + 1/13 + 1/25 + 1/49 + 1/97 < 1/6 + 1/6.2 + 1/6.4 + 1/6.8 + 1/6.16

1/7 + 1/13 + 1/25 +1/49 + 1/97 < 1 + ( 1/2+1/4/+1/6/+1/8+1/16)

1/7 + 1/13 + 1/25 + 1/49 + 1/97 < 1/6 x (\(\frac{16+8+4+2+1}{16}\))

1/7 + 1/13 + 1/25 + 1/49 + 1/97 < 16 x 31/16

1/7 + 1/13 + 1/25 + 1/49 + 1/97 < 31/96 < 31/31

Mà : 31/93 = 1/3

Vậy 1/7 + 1/13 + 1/25 + 1/49 + 1/97 < 1/3 

Ý bn đề vậy à ??? \(A=\frac{1}{7}+\frac{1}{13}+\frac{1}{25}+\frac{1}{49}+\frac{1}{97}....1\)

\(A=\frac{14}{98}+\frac{7}{91}+\frac{4}{100}+\frac{2}{98}+\frac{1}{97}< \frac{14}{91}+\frac{7}{91}+\frac{4}{91}+\frac{2}{91}+\frac{1}{91}=\frac{28}{91}=\frac{84}{273}< \frac{1}{3}=\frac{91}{273}\)

Vậy A < \(\frac{1}{3}\)

Hơi khó hiểu một chút nha bn

~Chúc bạn học tốt~

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mk nhé

bn

Ta có \(\frac{1}{7}< \frac{1}{6};\frac{1}{13}< \frac{1}{12};\frac{1}{25}< \frac{1}{24};\frac{1}{49}< \frac{1}{48};\frac{1}{97}< \frac{1}{96}\)

=> \(\frac{1}{7}+\frac{1}{13}+...+\frac{1}{97}< \frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}\)(chỗ này quy đồng nha ) 

=>\(\frac{1}{7}+\frac{1}{13}+...+\frac{1}{97}< \frac{31}{96}< \frac{32}{96}=\frac{1}{3}\)