Question

Chứng minh:

\(\frac{1}{4}+\frac{1}{16}+\frac{1}{36}+\frac{1}{64}+\frac{1}{100}+\frac{1}{144}+\frac{1}{169}<\frac{1}{2}\)

Answer 1

Bạn ơi , đề sai rồi , p/s cuối phải là 1/196 nhé . Mình giải cho luôn.Ta có 1/4 + 1/ 16 +1/36+1/100+1/144+1/196

= 1/2^2 + 1/ 4^2+ .........+1/12^2 + 1/14^2

= 1/ 2^2 . (1+1/2^2 +1/3^2+.............+1/6^2+1/7^2)<1/2^2. ( 1+ 1/1.2+  1/2.3+............+ 1/5.6+1/6.7) = 1/4 . (1+1 - 1/2+1/2 -1/3+..........+1/5 - 1/6 + 1/6 - 1/7) = 1/4. (1+1 - 1/7)=13/28 < 14/28=1/2

Vậy 1/4+1/16+ ........+1/196 < 1/2

Answer 2

chuẩn