\(P=\dfrac{3}{3.5}+\dfrac{3}{5.7}+...+\dfrac{3}{2015.2017}\)
\(P=3\left(\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{2015.2017}\right)\)
\(P=3.\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{2015}-\dfrac{1}{2017}\right)\)
\(P=\dfrac{3}{2}\left(\dfrac{1}{3}-\dfrac{1}{2017}\right)\)
\(P=\dfrac{3}{2}.\dfrac{2014}{6051}\)
\(P=\dfrac{1007}{2017}\)
Ta có :
\(P=\dfrac{3}{3.5}+\dfrac{3}{5.7}+.................+\dfrac{3}{2015.2017}\)
\(P.\dfrac{3}{2}=\dfrac{2}{3.5}+\dfrac{2}{5.7}+.................+\dfrac{2}{2015.2017}\)
\(P.\dfrac{3}{2}=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+.................+\dfrac{1}{2015}-\dfrac{1}{2017}\)
\(P.\dfrac{3}{2}=\dfrac{1}{3}-\dfrac{1}{2017}\)
\(P.\dfrac{3}{2}=\dfrac{2014}{6051}\)
\(\Rightarrow P=\dfrac{4028}{18153}\)
~ Chúc bn học tốt ~
P=1/2.(1/3-1/5+1/5-1/7+...+1/2015+1/2017)
P=1/2.(1/3-1/2017)
P=1/2.2014/6051
P=1007/6051
