Question

2/(5*7)+2/(7*9)+2/(9*11)+2/(11*13)+2/(13*15)+2/(15*17). Найдите значение выражения

Answer 1

2/7(1/5+1/9)+2/11(1/9+1/13)+2/15(1/13+1/17)=
=2/7*14/5*9+2/11*22/9*13+2/15*30/13*17=
=4/9(1/7*7/5+1/11*11/13)+2/15*30/13*17=
=4/9(1/5+1/13)+2/15*30/13*17=
=4/9*18/5*13+2/15*30/13*17=
=4/13(1/9*9/5+1/15*15/17)=4/13(1/5+1/17)=
=4/13*22/17*5=88/1135