Ta có:

\(\dfrac{2014+2015}{2015.2014}\)

\(=\dfrac{2014}{2015.2014}+\dfrac{2015}{2015.2014}\)

\(=\dfrac{1}{2015}+\dfrac{1}{2014}\)

Ta thấy:

\(\dfrac{1}{2015}+\dfrac{1}{2014}< \dfrac{1}{2014}+\dfrac{1}{2014}=\dfrac{2}{2014}=\dfrac{1}{1007}\)

\(\Rightarrow\dfrac{1}{2015}+\dfrac{1}{2014}< \dfrac{1}{1007}\)

\(\Rightarrow\dfrac{2014+2015}{2015.2014}< \dfrac{1}{1007}\)

nani?

1212;

1212;

1212.

k cho mình nhé.

1212

tk nhe@@@@@@@@@@@!!

aitk minh minh tk lai

bye

Ta so sánh từng số hạng : 

\(\frac{\sqrt{2}-\sqrt{1}}{1+2}=\frac{\left(\sqrt{2}-\sqrt{1}\right)\left(\sqrt{2}+\sqrt{1}\right)}{\left(1+2\right)\left(\sqrt{2}+\sqrt{1}\right)}=\frac{1}{\left(1+2\right)\left(\sqrt{2}+\sqrt{1}\right)}< \frac{1}{2}\)

\(\frac{\sqrt{3}-\sqrt{2}}{2+3}=\frac{\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}{\left(2+3\right)\left(\sqrt{3}+\sqrt{2}\right)}=\frac{1}{\left(2+3\right)\left(\sqrt{2}+\sqrt{3}\right)}< \frac{1}{2}\)

..........................................................................................................................................................................................

\(\frac{\sqrt{2015}-\sqrt{2014}}{2014+2015}=\frac{\left(\sqrt{2015}-\sqrt{2014}\right)\left(\sqrt{2015}+\sqrt{2014}\right)}{\left(2014+2015\right)\left(\sqrt{2015}+\sqrt{2014}\right)}=\frac{1}{\left(2014+2015\right)\left(\sqrt{2015}+\sqrt{2015}\right)}< \frac{1}{2}\)

Vì mỗi số hạng của M đều nhỏ hơn 1/2 nên M < 1/2

Bài này mình làm chưa đúng nhé :) Để lát mình làm cách khác.