Soma de Gauss
Calcule as seguintes somas:
a) S= 1+2+3+4+...+100
b) S=31+32+33+...500
c) S=10+20+30+...300
d) S=20+21+22+...+200
Soluções para a tarefa
Resposta:Segue as contas abaixo na explicação
Explicação passo-a-passo:
a) S= 1+2+3+4+...+100
a1=1,r=a2-a1-->r=2-1-->r=1,an=100,n=?,Sn=?
an=a1+(n-1).r Sn=(a1+an).n/2
100=1+(n-1).1 S100=(1+100).100/2
100=1+n-1 S100=101.100/2
n=100 S100=101.50
S100=5050
b) S=31+32+33+...500
a1=31,r=a2-a1-->r=32-31-->r=1,an=500,n=?,Sn=?
an=a1+(n-1).r Sn=(a1+an).n/2
500=31+(n-1).1 S470=(31+500).470/2
500=31+n-1 S470=531.470/2
500=30+n S470=531.235
500-30=30-30+n S470=124785
n=470
c)S=10+20+30+...300
a1=10,r=a2-a1-->r=20-10-->r=10,an=300,n=?,Sn=?
an=a1+(n-1).r Sn=(a1+an).n/2
300=10+(n-1).10 S30=(10+300).100/2
300=10+10n-10 S30=310.30/2
300=10n S30=310.15
n=300/10 S30=4650
n=30
d)S=20+21+22+...+200
a1=20,r=a2-a1-->r=21-20-->r=1,an=200,n=?,Sn=?
an=a1+(n-1).r Sn=(a1+an).n/2
200=20+(n-1).1 S181=(20+200).181/2
200=20+n-1 S181=220.181/2
200=19+n S181=110.181
200-19=19-19+n S181=19910
n=181