\(L_1=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+...+\dfrac{1}{2015.2016.2017}\)
\(L_1=\dfrac{1}{2}\left(\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+...+\dfrac{1}{2015.2016}-\dfrac{1}{2016.2017}\right)\)
\(L_1=\dfrac{1}{2}\left(\dfrac{1}{1.2}-\dfrac{1}{2016.2017}\right)\)
\(L_1=\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{2016.2017}\right)\)
\(L_1=\dfrac{1}{4}-\dfrac{1}{2.2016.2017}\)
\(L_2=1.2+2.3+...+2006.2007\)
\(3L_2=1.2.3+2.3.\left(4-1\right)+...+2006.2007.\left(2008-2005\right)\)
\(3L_2=1.2.3+2.3.4-1.2.3+...+2006.2007.2008-2005.2006.2007\)\(3L_2=2006.2007.2008\)
\(L_2=\dfrac{2006.2007.2008}{3}\)
\(pt\Leftrightarrow\left(\dfrac{1}{4}-\dfrac{1}{2.2016.2017}\right).x=\dfrac{2006.2007.2008}{3}\)
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