Question

Tìm x, biết

a) C=\(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{37.38.39}\)

Answer 1

C = \(2\cdot\left(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+...+\frac{1}{37\cdot38\cdot39}\right)\)

=> C = \(2\cdot\left(\left(1-\frac{1}{2}-\frac{1}{3}\right)+...+\left(\frac{1}{37}-\frac{1}{38}-\frac{1}{39}\right)\right)\)

=> C = \(2\cdot\left(1-\frac{1}{39}\right)=2\cdot\frac{38}{39}=\frac{76}{39}\)