Câu trả lời:
Ta có :
1/22 < 1/1.2
1/32 < 1/2.3
1/42 < 1/3.4
.................
1/502 < 1/49.50
\(\Rightarrow\) A - 1/12 < 1/1.2 + 1/2.3 + 1/3.4 + ..........+ 1/49.50
A - 1/1 < 1/1.2 + 1/2.3 + 1/3.4 + ...........+ 1/49.50
A - 1 < 1/1.2 + 1/2.3 + 1/3.4 + .............+ 1/49.50
\(\Rightarrow\) A < 1 + 1/1.2 + 1/2.3 + 1/3.4 + ........... 1/49.50 ( hai vế cùng cộng với 1 )
A < 1+ 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ........... + 1/49 - 1/50
A < 1 + 1 - 1/50
A < 2 - 1/50
Mà 2 - 1/50 < 2
\(\Rightarrow\) A < 2