Вычислите 1/(1*7)+1/(7*13)+1/(13*19)+1/(19*25)+...+1/(91/97)

 Попробуем так [latex]\dfrac{1}{1 \cdot 7} = \dfrac{1}{6} \cdot (1-\dfrac{1}{7}) , \\ \dfrac{1}{7 \cdot 13} = \dfrac{1}{6} \cdot (\dfrac{1}{7}-\dfrac{1}{13}) \\\\ ...\\\\ [/latex]       Получим   [latex] S = \dfrac{1}{6}(1-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{13}+...\dfrac{1}{97}) = \dfrac{1}{6} (1-\dfrac{1}{97}) = \dfrac{ 16}{ 97 }[/latex]