Question

cum se calculeaza?5+10+15+20+...+1000,dar,8+16+24+32+...+4000,si 30+60+90+...+900

Answer 1

5 + 10+ 15+...+1000= 5= 5×1; 10= 5×2; ... 1000=5× 200 Dupa cum se vede, fiecare isi numara locul. Deci in total sunt 200 termeni. Se calculeaza folosind termenul comun: 5×1 +5×2 +...+5×200= 5(1+2+...+200) Paranteza se calculeaza cu n(n+1)÷2 => 200×201÷2= 40200÷2 = 20100 Deci rezultatul este 20100×5 = 100500 Aplica asta si la urmatoarele subpuncte

Answer 2

$a)5+10+15+20+...+1000= \\ \\5(1+2+3+....+200)= \\ \\5 \frac{200(200+1)}{2} = 5*100*201=500*201=100500 \\ \\ \\ \\ b)8+16+24+...+4000= \\ \\ 8(1+2+3+...+500)= \\ \\ 8 \frac{500(500+1)}{2} = 8*250*501=1002000 \\ \\ \\ \\ c)30+60+90+...+900= \\ \\ 30(1+2+3+...+30)= \\ \\ 30 \frac{30(30+1)}{2}= 30*15*31=13950$