Question

1)  \(\dfrac{5}{13}\)  +\(\dfrac{-5}{17}\) +   \(\dfrac{-20}{41}\)   +   \(\dfrac{8}{13}\) +\(\dfrac{-21}{41}\)

2)  \(\dfrac{1}{5}\)  +  \(\dfrac{-2}{9}\)  +   \(\dfrac{-7}{9}\) +   \(\dfrac{4}{5}\)  +\(\dfrac{16}{17}\)

3) \(\dfrac{2}{3.5}\)  + \(\dfrac{2}{5.7}\) +\(\dfrac{2}{7.9}\)  +....................+ \(\dfrac{2}{99.101}\)

Answer 1

1: =5/13+8/13-20/41-21/41-5/17

=1-1-5/17=-5/17

2: =1/5+4/5-2/9-7/9+16/17

=16/17+1-1=16/17

3: =1/3-1/5+1/5-1/7+...+1/99-1/101

=1/3-1/101

=98/303