\(S=\dfrac{7}{3.5}+\dfrac{7}{5.7}+\dfrac{7}{7.9}+...+\dfrac{7}{2015.2017}\)
\(\dfrac{2}{7}S=\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{2015.2017}\)
\(\dfrac{2}{7}S=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{2015}-\dfrac{1}{2017}\)
\(\dfrac{2}{7}S=\dfrac{1}{3}-\dfrac{1}{2017}\)
\(\dfrac{2}{7}S=\dfrac{2014}{6051}\)
\(S=\dfrac{4028}{42357}\)
\(S=\dfrac{7}{3.5}+\dfrac{7}{5.7}+\dfrac{7}{7.9}+...+\dfrac{7}{2015.2107}\)
\(S=\dfrac{7}{2}\left(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{2015.2017}\right)\)
\(S=\dfrac{7}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}...+\dfrac{1}{2015}-\dfrac{1}{2017}\right)\)
\(S=\dfrac{7}{2}\left(\dfrac{1}{3}-\dfrac{1}{2017}\right)\)
\(S=\dfrac{7}{2}.\dfrac{2014}{6051}\)
\(S=\dfrac{4028}{42357}\)
S= 7/3.5 + 7/5.7 + 7/7.9 +...+ 7/2015.2017
= 7/2 .( 2/3.5 + 2/5.7 + 2/7.9 +...+ 2/2015.2017 )
=7/2 .( 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 +...+ 1/2015 - 1/2017 )
=7/2 .( 1/3 - 1/2017 )
= 7/2 . 2014/6051
