Question

Tính giá trị của biểu thức

A=3/1.4+3/4.7+3/7.10+...+3/40.43+3/2015.2016

Answer 1

A = \(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}+...+\dfrac{3}{40\cdot43}+\dfrac{3}{2015\cdot2016}\)

A = \(\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}+...+\dfrac{3}{40\cdot43}\right)+\left(\dfrac{1}{2015\cdot2016}\cdot3\right)\)

A = \(\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{40}-\dfrac{1}{43}\right)+\left(\left(\dfrac{1}{2015}-\dfrac{1}{2016}\right)\cdot3\right)\)

A = \(\left(1-\dfrac{1}{43}\right)+\dfrac{1}{1354080}=\dfrac{42}{43}+\dfrac{1}{1354080}=\dfrac{56871403}{58225440}\)