Question

\(B=\frac{2}{1x3}+\frac{2}{3x5}+\frac{2}{5x7}+.....+\frac{2}{57x59}\)

Answer 1

^{\(B=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+........+\frac{2}{57.59}\)}

\(B=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-.........-\frac{1}{59}\)

\(B=1-\frac{1}{59}\)

\(B=\frac{59}{59}-\frac{1}{59}=\frac{58}{59}\)

Vậy B = \(\frac{58}{59}\)

Lưu ý: Dấu "." là dấu nhân

Answer 2

\(B=\frac{2}{1.3}+\frac{1}{3.5}+\frac{2}{5.7}+...+\frac{1}{57.59}\)

\(B=1.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{57}-\frac{5}{59}\right)\)

\(B=1.\left(1-\frac{1}{59}\right)\)

\(B=1.\frac{58}{59}\)

\(B=\frac{58}{59}\)