Question

Tính nhanh:1/3+1/6+1/10+ +1/78 xin được giúp đỡ Cảm ơn

Answer 1

Đặt \(A=\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+....+\dfrac{1}{78}\)

⇒\(\dfrac{1}{2}A=\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{156}\)

⇒\(\dfrac{1}{2}A=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{12.13}\)

⇒\(\dfrac{1}{2}A=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}+...+\dfrac{1}{12}-\dfrac{1}{13}\)

⇒\(\dfrac{1}{2}A=\dfrac{1}{2}-\dfrac{1}{13}\)\(=\dfrac{11}{26}\)

⇒\(A=\dfrac{11}{26}:\dfrac{1}{2}\)

⇒\(A=\dfrac{11}{13}\)