= 3.(3/3 - 3/4 + 3/4 - 3/5 + 3/5 - 3/6 +.....+ 3/277 - 3/278 + 3/278 - 3/279)
= 3.(3/3 - 3/279 )
= 3.92/93
= 187/93
Mình cũg không chắc chắn là 100% đâu bạn nên dò lại nhé 
Đặt biểu thức là \(A\)
\(A=\dfrac{3}{3.4}+\dfrac{3}{4.5}+\dfrac{3}{5.6}+...+\dfrac{3}{278.279}\)
\(\Leftrightarrow\dfrac{1}{3}A=\dfrac{1}{3}\left(\dfrac{3}{3.4}+\dfrac{3}{4.5}+\dfrac{3}{5.6}+...+\dfrac{3}{278.279}\right)\)
\(\Leftrightarrow\dfrac{1}{3}A=\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+...+\dfrac{1}{278.279}\)
\(\Leftrightarrow\dfrac{1}{3}A=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{278}-\dfrac{1}{279}\)
\(\Leftrightarrow\dfrac{1}{3}A=\dfrac{1}{3}-\dfrac{1}{279}\)
\(\Leftrightarrow\dfrac{1}{3}A=\dfrac{93}{279}-\dfrac{1}{279}\)
\(\Leftrightarrow\dfrac{1}{3}A=\dfrac{92}{279}\)
\(\Leftrightarrow A=\dfrac{92}{279}:\dfrac{1}{3}\)
\(\Leftrightarrow A=\dfrac{92}{279}.3\)
\(\Leftrightarrow A=\dfrac{92}{93}\)