Question

B=1/3+1/15+1/35+...+1/97×99 Ai làm nhanh mik tk cho nkaa:3

Answer 1

\(B=\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{35}+...+\dfrac{1}{97\times99}\)

\(=\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{97.99}\)

\(=\dfrac{1}{2}.\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{97.99}\right)\)

\(=\dfrac{1}{2}.\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)

\(=\dfrac{1}{2}.\left(1-\dfrac{1}{99}\right)\)

\(=\dfrac{1}{2}.\dfrac{98}{99}\)

\(=\dfrac{49}{99}\)

dấu \(.\) là dấu \(\times\)