Question

tính nhanh : B =\(\frac{4}{1\cdot2}+\frac{4}{2\cdot3}+\frac{4}{3\cdot4}+.......+\frac{4}{29\cdot30}\)

Answer 1

\(B=4.\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{29.30}\right)\)

\(B=4.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{29}-\frac{1}{30}\right)\)

\(B=4.\left(1-\frac{1}{30}\right)\)

\(B=4.\frac{29}{30}\)

\(B=\frac{58}{15}\)

Answer 2

\(B=4\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{29}-\frac{1}{30}\right)\) 

\(=4\left(1-\frac{1}{30}\right)\) 

\(=4.\frac{29}{30}=\frac{58}{15}\) 

Vậy B= \(\frac{58}{15}\)