Question

calculati a) 2+3+4+....+99+100+101+102 b) 7+8+9+....+79+80+81 c) 25+26+27+....+127+128+129 Ajutati-ma urgent

Answer 1

a) 2+3+4+....+99+100+101+102
S=S1-1
S1=1+2+3+.....+102=(102×103):2= 
(suma Gauss cu formula de calcul S=[n×(n+1)]:2
S=5253-1
S=5252

b) 7+8+9+....+79+80+81
S=S1-S2
S1=1+2+3+4+.......+81=(81×82):2=  (suma Gauss cu formula de calcul S=[n×(n+1)]:2
S2=1+2+3+3+4+5+6=(6×7):2=21  (suma Gauss cu formula de calcul S=[n×(n+1)]:2
S=3321-21=3300
S=3300

c) 25+26+27+....+127+128+129
S=S1-S2
S1=1+2+3+.....+129=(129×130):2=8385  (suma Gauss cu formula de calcul S=[n×(n+1)]:2
S2=1+2+3+4+.....+24=(24×25):2=300    (suma Gauss cu formula de calcul S=[n×(n+1)]:2
S=8085