Răspuns:
Explicație pas cu pas:
Ne folosim de punctul a
Astfel vom avea
[tex]\frac{1}{1\cdot 6} =\frac{1}{5} (\frac{1}{1}-\frac{1}{6})[/tex]
[tex]\frac{1}{6\cdot 11} =\frac{1}{5} (\frac{1}{6}-\frac{1}{11})[/tex]
...
[tex]\frac{1}{(5n+1)\cdot (5n+6)} =\frac{1}{5} (\frac{1}{5n+1}-\frac{1}{5n+6})[/tex]
Inlocuim in suma noastra si vom avea
[tex]\frac{1}{5} (\frac{1}{1} -\frac{1}{6} )+\frac{1}{5} (\frac{1}{6} -\frac{1}{11} )+...+\frac{1}{5} (\frac{1}{5n+1}-\frac{1}{5n+6}) =\\\frac{1}{5} (\frac{1}{1} -\frac{1}{6}+\frac{1}{6} -\frac{1}{11} +...+\frac{1}{5n+1}-\frac{1}{5n+6})=\frac{1}{5}( \frac{1}{1} -\frac{1}{5n+6})[/tex]
[tex]\frac{1}{5}( \frac{1}{1} -\frac{1}{5n+6})=\frac{1}{5} \cdot \frac{5n+5}{5n+6}[/tex]
[tex]\frac{5n+5}{5n+6}<1[/tex] este fractie subunitara⇒[tex]\frac{1}{5}\cdot \frac{5n+5}{5n+6}<\frac{1}{5}[/tex]
