3/1·4 + 3/4·7 + 3/7·10 + .. + 3/97·100 =
= (4-1)/1·4 + (7-4)/4·7 + (10-7)/7·10 + .. + (100-97)/97·100
= 4/1·4 - 1/1·4 + 7/4·7 - 4/4·7 + 10/7·10 - 7/7·10 + .. + 100/97·100 - 97/97·100
simplificam
= 1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + .. + 1/97 - 1/100
reducem termenii asemenea
= 1 - 1/100
= (100 - 1)/100
= 99/100
