-noi trebuie sa cautam sa-l scriem pe 8/9 ca o suma de elemente de forma 1/n-1/n+1 si o sa se rezolve in felul urmator:
[tex] \frac{1}{2^2}+ \frac{1}{3^2}+...+ \frac{1}{9^2}\ \textless \ \frac{1}{1\cdot2}+ \frac{1}{2\cdot3}+...+ \frac{1}{8\cdot9} \\ \\ \frac{1}{2^2}\ \textless \ \frac{1}{1\cdot2}~adevarat \\ \frac{1}{3^2}\ \textless \ \frac{1}{2\cdot3}~adevarat \\ . \\ . \\ . \\ \frac{1}{9^2}\ \textless \ \frac{1}{8\cdot9}~adevarat, \\ -din~toate~inegalitatile~de~mai~sus~rezulta~concluzia. [/tex]
