Question

[Vũ Châu]

cho s=7/4+17/9+31/16+...+799/400. Chứng minh s > 37

Answer 1

[Akai Haruma]

Lời giải:

$S=(2-\frac{1}{4})+(2-\frac{1}{9})+(2-\frac{1}{16})+...+(2-\frac{1}{400})$

$=(2+2+2+....+2)-(\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+...+\frac{1}{400})$

$=2.19-(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{20^2})$

$> 38-(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{19.20})$
$=38-(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{19}-\frac{1}{20})$
$=38-(1-\frac{1}{20})=37+\frac{1}{20}> 37$
Ta có đpcm.