Matematică
gabipav
8

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.

+0
(1) Răspunsuri
salti666

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

Adaugă răspuns