Question

a) S= 1 + 4 + 7 + ............ + 301
b) S= 51 + 52 + ..... + 100
c) S= 2 + 4 + 6 + ......+ 500
d) S= 5 + 10 + 15 + .............. 2000.
REZOLVAREA COMPLETA .Mercii

Answer 1

a) S= 1 + 4 + 7 + ............ + 301 =1+(1+3*1)+(1+3*2)+...+(1+3*100)=1+1+....1+3*(1+2+3+...+100=1*100+3*100*101/2=100+300*101/2=100+15150=15250
b) S= 51 + 52 + ..... + 100=51+(51+1*1)+(51+1*2)+...+(51+1*49)=51+51+51++...+51+51(1+2+..+49)=51*49+51*49*50/2=51*49+51*49*25=51*49*(1+25)=51*49*26=11934
c) S= 2 + 4 + 6 + ......+ 500=2(1+2+3+...+250)=2*250*251/2=62750
d) S= 5 + 10 + 15 + .............. 2000=5(1+2+3+...+400)=5*400*401/2=401000