Question

[Công Chúa Hoa Anh Đào]

Chứng minh rằng

1/5+1/13+1/25+1/41+1/61+1/85+1/113 < 2

Bài này mk ko hiểu.Giải hộ mk vs >.<

Answer 1

[yingzie]

đặt A=\(\dfrac{1}{5}+\dfrac{1}{13}+\dfrac{1}{25}+\dfrac{1}{41}+\dfrac{1}{61}+\dfrac{1}{85}+\dfrac{1}{113}\)

        = \(\dfrac{1}{5}+(\dfrac{1}{13}+\dfrac{1}{25}+\dfrac{1}{41})+(\dfrac{1}{61}+\dfrac{1}{85}+\dfrac{1}{113})\)

=> A< \(\dfrac{1}{5}+(\dfrac{1}{12}+\dfrac{1}{12}+\dfrac{1}{12})+(\dfrac{1}{60}+\dfrac{1}{60}+\dfrac{1}{60})\)

     A<\(\dfrac{1}{5}+\dfrac{1}{4}+\dfrac{1}{20}\)=\(\dfrac{1}{2}\)

vậy A<\(\dfrac{1}{2}\),<2=> A<2 (đpcm)