Question

[Sao băng tốc độ]

Điền dấu vào chỗ trống : 

1/7 + 1/13+ 1/25 + 1/49 + 1/97 ........ 1/3

Answer 1

[thien ty tfboys]

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

Answer 2

[Nguyễn Đình Dũng]

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