Спримером 1+1/10*11+1/11*12+1/12*13+1/13*14+1/14*15+1/15*16

1/n - 1/(n+1) = (n+1 - n)/n(n+1) = 1/n(n+1) 
для одного примера 1/10*11= 1/10 - 1/11
1+1/10*11+1/11*12+1/12*13+1/13*14+1/14*15+1/15*16 = 1 + (1/10 - 1/11)  + (1/11 - 1/12) + (1/12 - 1/13) + (1/13 - 1/14) + (1/14 - 1/15) + (1/15 - 1/16) = 1 + 1/10 - 1/16 = 1 + 8/80 - 5/80 = 1 + 3/80 = 1 3/80