Question

[Nguyễn Thiên An]

Giúp mình với 

Answer 1

[Akai Haruma]

Lời giải:

a.

$\frac{-12345}{12344}=\frac{-(12344+1)}{12344}=-1+\frac{-1}{12344}$

$\frac{-12346}{12345}=\frac{-(12345+1)}{12345}=-1+\frac{-1}{12345}$

Hiển nhiên $\frac{1}{12344}> \frac{1}{12345}$

$\Rightarrow \frac{-1}{12344}< \frac{-1}{12345}$

$\Rightarrow -1+ \frac{-1}{12344}< -1+\frac{-1}{12345}$

$\Rightarrow \frac{-12345}{12344}< \frac{-12346}{12345}$

b.

$\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}$
$< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}$

$=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{100-99}{99.100}$

$=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}$

$=1-\frac{1}{100}<1$