Question

Tính GTBT sau:

C=\(\frac{1}{1.3}\)+\(\frac{1}{3.5}\)+\(\frac{1}{5.7}\)+...+\(\frac{1}{35.37}\)

Ghi chú: Dấu . là dấu nhân nha m.n

Answer 1

\(C=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{35.37}\)

\(C=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{35.37}\right)\)

\(C=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{35}-\frac{1}{37}\right)\)

\(C=\frac{1}{2}.\left(1-\frac{1}{37}\right)\)

\(C=\frac{1}{2}.\frac{36}{37}\)

\(C=\frac{18}{37}\)

Answer 2

\(C=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{35.37}\)

\(C=\frac{1}{2}\cdot\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{35}-\frac{1}{37}\right)\)

\(C=\frac{1}{2}\cdot\left(1-\frac{1}{37}\right)\)

\(C=\frac{1}{2}\cdot\frac{36}{37}=\frac{18}{37}\)

Vay C = \(\frac{18}{37}\)

Answer 3

\(C=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{35.37}\)

\(C=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{35}-\frac{1}{37}\right)\)

\(C=\frac{1}{2}.\left(1-\frac{1}{37}\right)\)

\(C=\frac{1}{2}.\frac{36}{37}\)

\(C=\frac{18}{37}\)