[tex]\displaystyle\\1)\\\\\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+\frac{5}{6}=\boxed{\sum _{k=1}^{5}{\frac{k}{k+1}}}\\\\\\2)\\\\ -11+12-13+14-15+16=\boxed{\sum _{k=1}^{6}{(-1)^k\cdot(10+k)} }[/tex]
[tex]\displaystyle\\3)\\9-16+25-36+49-64=\boxed{\sum_{k=1}^{6}{(-1)^{k+1}\cdot(k+2)^2}}\\\\\\4)\\\\3+\frac{3}{2}+1+\frac{3}{4}+\frac{3}{5}=\frac{3}{1}+\frac{3}{2}+\frac{3}{3}+\frac{3}{4}+\frac{3}{5}=\boxed{\sum_{k=1}^{5}{\frac{3}{k}}}[/tex]
