Question

[Nguyễn Đắc Phúc An]

Chứng minh rằng:B=\(\dfrac{36}{1.3.5}+\dfrac{36}{3.5.7}+\dfrac{36}{5.7.9}+...+\dfrac{36}{25.27.29}< 3\)

Ai làm đúng mình tick cho nha

Answer 1

[Nguyễn Thanh Hằng]

Ta có :

\(B=\dfrac{36}{1.3.5}+\dfrac{36}{3.5.7}+\dfrac{36}{5.7.9}+...............+\dfrac{36}{25.27.29}\)

\(B=9\left(\dfrac{4}{1.3.5}+\dfrac{4}{3.5.7}+\dfrac{4}{5.7.9}+.............+\dfrac{4}{25.27.29}\right)\)

\(B=9\left(\dfrac{1}{1.3}-\dfrac{1}{3.5}+\dfrac{1}{3.5}-\dfrac{1}{5.7}+\dfrac{1}{5.7}-\dfrac{1}{7.9}+...........+\dfrac{1}{25.27}-\dfrac{1}{27.29}\right)\)

\(B=9\left(\dfrac{1}{1.3}-\dfrac{1}{27.29}\right)\)

\(B=9\left(\dfrac{1}{3}-\dfrac{1}{783}\right)\)

\(B=9.\dfrac{1}{3}-9.\dfrac{1}{783}\)

\(B=3-\dfrac{9}{783}< 3\)

\(\Rightarrow B< 3\rightarrowđpcm\)