Question

Calculati . 1+2+3+...+99 1+3+5+...+99 2+4+6+...+100. 4+9+14+19+...+204 1+4+7+10+...+100 3+6+9+...+360.

Answer 1

1.
1+2+3+...+99 1+3+5+...+99 = 99*100/2=99*50= 4950
2.
2+4+6+...+100= 2*(1+2+3+...+50)= 2*50*51/2=2*51*25=50*51=2550
3.
4+9+14+19+...+204 = (204+4)*41/2=208*41/2=4264
a1=5*1-1=4
a2=5*2-1=9
5*n-1=204
5*n=205
n=205:5; n=41
4.
1+4+7+10+...+100 = (100+1)*34/2=101*17=1717
a1=3*1-2=1
a2=3*2-2=4
an=3*n-2
3*n-2=100
100=3*n-2
3n=100+2
3n=102 |:3
n=34
5.
3+6+9+...+360.=3*(1+2+3+....+120)=3*120*121/2=21780