1/5 - 3/7 + 5/9 - 2/11 + 7/13 - 9/16 -7/13 + 2/11 - 5/9 +3/7 -1/5
= ( 1/5-1/5) + (-3/7 +3/7 ) + (5/9 - 5/9 ) + (-2/11+2/11 ) + ( 7/13 - 7/13 ) - 9/16
= 0 + 0 + 0 + 0 + 0 +0 - 9/16
= -9/16
\(\dfrac{1}{5}-\dfrac{3}{7}+\dfrac{5}{9}-\dfrac{2}{11}+\dfrac{7}{13}-\dfrac{9}{16}-\dfrac{7}{13}+\dfrac{2}{11}-\dfrac{5}{9}+\dfrac{3}{7}-\dfrac{1}{5}\)
\(=\)\(\left(\dfrac{3}{7}+\dfrac{-3}{7}\right)+\left(\dfrac{1}{5}-\dfrac{1}{5}\right)+\left(\dfrac{5}{9}-\dfrac{5}{9}\right)+\left(\dfrac{-2}{11}+\dfrac{2}{11}\right)+\left(\dfrac{7}{13}-\dfrac{7}{13}\right)+\dfrac{9}{16}\)
\(=0+0+0+0+0+\dfrac{9}{16}\)
\(=\dfrac{9}{16}\)
