Question

Cho B= 5^2/10^2+5^2/11^2+...+5^2/99^2 chứng minh B > 9/4

Answer 1

Ta có:

B = \(\frac{5^2}{10^2}\) + \(\frac{5^2}{11^2}\)+ ... + \(\frac{5^2}{99^2}\)

B = 5². (\(\frac{1}{10^2}\) + \(\frac{1}{11^2}\)+ ... + \(\frac{1}{99^2}\))

⇒ B > 5². (\(\frac{1}{10.11}\) + \(\frac{1}{11.12}\)+ ... + \(\frac{1}{99.100}\))

= 5². (\(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{99}-\frac{1}{100}\))

= 5². (\(\frac{1}{10}-\frac{1}{100}\))

= 25.\(\frac{9}{100}\)

= \(\frac{9}{4}\)

⇒ B > \(\frac{9}{4}\) (ĐPCM)