Question

 

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

Answer 1

\(\frac{2}{3x5}+\frac{2}{5.7}+\frac{2}{7x9}+...+\frac{2}{99x101}=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}=\frac{1}{3}-\frac{1}{101}=\frac{98}{303}\)
\(\frac{\Rightarrow1}{15}+\frac{1}{35}+...+\frac{1}{9999}=\frac{98}{303x2}=\frac{49}{303}\)