Question

1/15+1/35+1/63+1/99...+1/9999

 

Answer 1

\(\frac{49}{303}\)

Answer 2

\(\frac{1}{15}+\frac{1}{35}+....+\frac{1}{9999}=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-....-\frac{1}{101}\right)=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{101}\right)=\frac{49}{303}\)

Answer 3

1/15+1/35+...+1/9999

=1/2.(1/3-1/5+1/5-...-1/101)

=1/2.(1/3-1/101)

=49/303