Question

\(B=\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{...2}{9999}=?\)

Answer 1

=2/1.3+2/3.5+2/5.7+....+2/99.101

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

=1-1/101

=100/101

Answer 2

\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+...+\frac{2}{99.101}\)

\(=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\)

\(=1-\frac{1}{101}=\frac{100}{101}\)