Răspuns:
A)50
B)52
Explicație pas cu pas:
a) S1=2+4+6+...+100
S1=2(1+2+3+...+50)=2*50*(50+1):2=50*51=2550
S2=1+3+5+...+99
S2=99+97+...+1
-----------------------
2S2=100+100+...+100
numar termeni: (99-1):2+1=98:2+1=49+1=50
2S2=100*50 => S2=100*50:2=50*50=2500
S1-S2=2550-2500=50
b)
S1=3+7+11+...+99+103
S1=103+99+...+7+3
-----------------------------
2S1=106+106+...+106
numar termeni: (103-3):4+1=100:4+1=25+1=26
2S1=106*26=53*26
S2=1+5+9+...+97+101
S2=101+97+...+5+1
-----------------------------
2S2=102+102+...+102
numar termeni: (101-1):4+1=100:4+1=25+1=26
2S2=102*26 => S2=102*26:2 => S2=51*26
S1-S2=53*26-51*26=26*(53-51)=26*2=52
pentru a afla numarul de termeni:
(cel mai mare numar -cel mai mic numar): din cat in cat se repeta+1
in general este: (ultimul-primul): din cat in cat se repeta+1
ca sa aflii din cat in cat se repeta=scazi primul numar din al doilea
