Question

Bai 5. Tinh nhanh

a, \(\dfrac{1}{5.8}+\dfrac{1}{8.7}+\dfrac{1}{11.14}+.......+\dfrac{1}{605.606}\)

b,\(\left(\dfrac{1}{10}-1\right)\left(\dfrac{1}{11}-1\right)\left(\dfrac{1}{12}-1\right)....\left(\dfrac{1}{2012}-1\right)\)

Answer 1

Mk ko biết nhưng mk chúc bn sớm tìm đc câu trả lời

Answer 2

b)

\(\left(\dfrac{1}{10}-1\right)\left(\dfrac{1}{11}-1\right)\left(\dfrac{1}{12}-1\right)...\left(\dfrac{1}{2012}-1\right)\\ =\dfrac{-9}{10}\cdot\dfrac{-10}{11}\cdot\dfrac{-11}{12}\cdot...\cdot\dfrac{-2011}{2012}\\ =\left(-1\right)\cdot\dfrac{9}{10}\cdot\left(-1\right)\cdot\dfrac{10}{11}\cdot\left(-1\right)\cdot\dfrac{11}{12}\cdot...\cdot\left(-1\right)\cdot\dfrac{2011}{2012}\\ =\left[\left(-1\right)\cdot\left(-1\right)\cdot...\cdot\left(-1\right)\right]\cdot\left(\dfrac{9}{10}\cdot\dfrac{10}{11}\cdot\dfrac{11}{12}\cdot...\cdot\dfrac{2011}{2012}\right)\\ =\left[\left(-1\right)\cdot\left(-1\right)\cdot...\cdot\left(-1\right)\right]\cdot\dfrac{9}{2012}\)

(Có tất cả 2003 thừa số -1)

\(=\left(-1\right)\cdot\dfrac{9}{2012}=\dfrac{-9}{2012}\)