Question

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

Answer 1

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