Question

Chứng minh rằng 1/2mũ 2 + 1/4mũ 2+1/6mũ 2 + ...+ 1/100 mũ 2 <1/2

 

Answer 1

`A= 1/(2 ^ 2) + 1/(4 ^ 2) + 1/(6 ^ 2) +.............+ 1/(100^ 2)`

`A= 1/(2^ 2) .( 1 + 1/(2 ^ 2) + 1/(3 ^ 2) +..............+ 1/(50^ 2 )< 1/4( 1 + 1/(1.2) + 1/(2.3) +........+ 1/(49.50) )`

`A< 1/4 .( 1 + 1 - 1/2 + 1/2 - 1/3 +........+ 1/49 - 1/50 )`

`A< 1/4 . (2 - 1/50)`

`A < 99/200 < 100/200 = 1/2`

`Rightarrow A < 1/2`

Vậy `A<1/2`