Solusi

Misalkan $X=\large{\frac{1}{1980}+\frac{1}{1981}+...+\frac{1}{2001}}$

Batas bawah

$\large{\frac{1}{1980}+\frac{1}{1981}+...+\frac{1}{2001}}\lt\large{\frac{1}{1980}+\frac{1}{1980}+...+\frac{1}{1980}}$

$X\lt\large{\frac{1}{1980}+\frac{1}{1980}+...+\frac{1}{1980}}$

$X\lt\large{\frac{22}{1980}}$

$X\lt\large{\frac{1}{90}}$

$A\gt90$

Batas atas

$\large{\frac{1}{1980}+\frac{1}{1981}+...+\frac{1}{2001}}\gt\large{\frac{1}{2001}+\frac{1}{2001}+...+\frac{1}{2001}}$

$X\gt\large{\frac{1}{2001}+\frac{1}{2001}+...+\frac{1}{2001}}$

$X\gt\large{\frac{22}{2001}}$

$A\lt\large{\frac{2001}{22}}$

$A\lt90\large{\frac{21}{22}}$

Dari batas atas dan batas bawah kita dapat $90 \lt A \lt 90\large{\frac{21}{22}}$

Cukup jelas $\lfloor A \rfloor = 90$