Question

Tính : 

\(P=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{47.49}\)

Answer 1

\(P=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{47.49}\)

\(P=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-...+\frac{1}{47}-\frac{1}{49}\right)\)

\(P=\frac{1}{2}.\left(1-\frac{1}{49}\right)\)

\(P=\frac{1}{2}.\frac{48}{49}\)

\(P=\frac{24}{49}\)

Answer 2

\(P=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{47.49}\)

\(P=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{47.49}\right)\)

\(P=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{47}-\frac{1}{49}\right)\)

\(P=\frac{1}{2}.\left(1-\frac{1}{49}\right)\)

\(P=\frac{1}{2}.\frac{48}{49}\)

\(P=\frac{24}{49}\)