Question

,buna dimineata,cine ma ajuta cu 4 sume ale lui.gauss? DAU COROANA!!

a)2+4+6+8+.....+180=
b)3+6+9+12+.....+240=
c)5+10+15+.....+150=
d)1+3+5+.....+403=​​

Answer 1

a)

180 = 2 + (n - 1)*2 = 2 + 2n - 2 = 2n

n = 180 : 2 = 90 termeni in suma

S = 90*(2 + 180)/2 = 90*182/2 = 90*91 = 8190

___________

b)

240 = 3 + (n - 1)*3 = 3 + 3n - 3 = 3n

n = 240 : 3 = 80 termeni in suma

S = 80*(3 + 240)/2 = 80*243/2 = 40*243 = 9720

____________

c) 150 = 5 + (n - 1)*5 = 5 + 5n - 5 = 5n

n = 150 : 5 = 30 termeni in suma

S = 30*(5 + 150)/2 = 30*155/2 = 15*155 = 2325

____________

d)

403 = 1 + (n - 1)*2 = 1 + 2n - 2 = 2n - 1

2n = 403 + 1 = 404

n = 404 : 2 = 202

S = 202*(1 + 403)/2 = 202*404/2 = 202*202 = 40804

Sper ca te-am ajutat!

Bafta!