Question

B=2^2/1*3+2^2/3*5+2^2/5*7+...+2^2/99*101

Answer 1

\(B=\dfrac{2^2}{1.3}+\dfrac{2^2}{3.5}+\dfrac{2^2}{5.7}+...+\dfrac{2^2}{99.101}\)

\(B=\dfrac{4}{1.3}+\dfrac{4}{3.5}+\dfrac{4}{5.7}+...+\dfrac{4}{99.101}\)

\(B=\dfrac{1}{2}\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{99.101}\right)\)

\(B=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\)

\(B=\dfrac{1}{2}\left(1-\dfrac{1}{101}\right)\)

\(B=\dfrac{1}{2}.\dfrac{100}{101}\)

\(B=\dfrac{50}{101}\)