Question

S= 3/5 + 6/10 + 9/15 +12/20 +.....+6042/10070+6045/10075 (vă rog sa imi explicați cum trebuie procedat la aces exercițiu)​

Answer 1

avem 2015 termeni

3/5=(5-2)/5=5/5-2/5= 1-2/5

6/10=(10-4)/10= 10/10-4/10= 1-2/5 (4/10 simplificam cu 2)

9/15= (15-6)/15= 15/15-6/15= 1-2/5 (6/15 simplificam cu 3)

...

6042/10070= (10070-4028)/10070= 10070/10070-4028/10070= 1-2/5 (4028/10070 simplificam cu 2014)

6045/10075=(10075-4030)/10075= 10075/10075-4030/10075= 1-2/5 (4030/10075 simplificam cu 2015)

3/5+6/10+9/15+12/20+.. +6042/10070+6045/10075= 1-2/5+1-2/5+1-2/5+1-2/5+...+1-2/5+1-2/5= 1*2015-2015*2/5= 2015-806= 1209