Question

Tính nhanh :

C = \(\frac{3}{2.3.4}+\frac{3}{3.4.5}+\frac{3}{4.5.6}+....+\frac{3}{98.99.100}\)

Answer 1

C = \(\frac{3}{2.3.4}+\frac{3}{3.4.5}+...+\frac{3}{98.99.100}\)

C = \(3.\frac{1}{2}.\left(\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{98.99.100}\right)\)

C = \(\frac{3}{2}.\left(\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{100-98}{98.99.100}\right)\)

C = \(\frac{3}{2}.\left(\frac{4}{2.3.4}-\frac{2}{2.3.4}+\frac{5}{3.4.5}-\frac{3}{3.4.5}+...+\frac{100}{98.99.100}-\frac{98}{98.99.100}\right)\)

C = \(\frac{3}{2}.\left(\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{98.99}-\frac{1}{99.100}\right)\)

C = \(\frac{3}{2}.\left(\frac{1}{2.3}-\frac{1}{99.100}\right)\)

C = \(\frac{3}{2}.\frac{1649}{9900}\)

C = \(\frac{1649}{6600}\)