Question

4/9x11 +4/11x13+ 4/13x15+....+4/97x994/9x11 +4/11x13+ 4/13x15+....+4/97x99 /=Phần Các cậu trả lời nhanh giúp tớ ạ,cảm ơn các cậu nhiều

Answer 1

\(\dfrac{4}{9\cdot11}+\dfrac{4}{11\cdot13}+...+\dfrac{4}{97\cdot99}\)

\(=2\left(\dfrac{2}{9\cdot11}+\dfrac{2}{11\cdot13}+...+\dfrac{2}{97\cdot99}\right)\)

\(=2\left(\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)

\(=2\cdot\left(\dfrac{1}{9}-\dfrac{1}{99}\right)\)

\(=2\cdot\dfrac{10}{99}=\dfrac{20}{99}\)