đặt A = $\frac{3}{1^{2}.2^{2}}$+$\frac{5 }{ 2^{2}.3^{2}}$+$\frac{7}{3^{2}.4^{2}}$+...+$\frac{19}{9^{2}.10^{2}}$
=$\frac{2^{2}-1^{2}}{1^{2}.2^{2}}$+$\frac{3^{2}- 2^{2} }{ 2^{2}.3^{2}}$+$\frac{4^{2}- 3^{2}}{3^{2}.4^{2}}$+...+$\frac{10^{2}- 9^{2} }{9^{2}.10^{2}}$
=$\frac{1}{1^{2}}$ - $\frac{1}{2^{2}}$ + $\frac{1}{2^{2}}$ - $\frac{1}{3^{2}}$ + $\frac{1}{3^{2}}$ - $\frac{1}{4^{2}}$ + ...+ $\frac{1}{9^{2}}$ - $\frac{1}{10^{2}}$
=$\frac{1}{1^{2}}$ - $\frac{1}{10^{2}}$
=$\frac{10^{2} - 1^{2}}{1^{2}. 10^{2}}$
=$\frac{100-1}{1.100}$
=$\frac{99}{100}$
DO 99<100
⇒$\frac{99}{100}$ < 1
⇒A < 1
XIN 5*
