Question

Cho A=1/4+1/9+1/16+...+1/18+1/100.CHứng minh A>65/132

Answer 1

đề bài bạn sai vì theo như quy luật thì :

A=\(\dfrac{1}{4}+\dfrac{1}{9}+\dfrac{1}{16}+...+\dfrac{1}{81}+\dfrac{1}{100}\)

\(\dfrac{1}{4}>\dfrac{1}{3.2}\)

\(\dfrac{1}{9}>\dfrac{1}{3.4}\)

\(\dfrac{1}{16}>\dfrac{1}{4.5}\)

.

.

.

\(\dfrac{1}{81}>\dfrac{1}{9.10}\)

\(\dfrac{1}{100}>\dfrac{1}{10.11}\)

A > \(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{9.10}+\dfrac{1}{10.11}\)

A > \(\dfrac{1}{2}+\dfrac{1}{11}\) =\(\dfrac{13}{22}\)

mà \(\dfrac{13}{22}\)>\(\dfrac{65}{132}\) ; A>\(\dfrac{13}{22}\)

Vậy A>\(\dfrac{65}{132}\)