Question

ajutatima va rog frumoss gasiti si scoateti un factor comun ,cand calculati urmatoarele sume b 8+16+24+32+.......+4000 e 4+8+12+16+........400

Answer 1

$\displaystyle a).8+16+24+32+...+4000 =8(1+2+3+...+500)= \\ \\ =8 \times \frac{500(500+1)}{2} =8 \times \frac{500 \times 501}{2} =8 \times \frac{250500}{2} = \\ \\ =8 \times 125250=1002000$

$\displaystyle b).4+8+12+16+...+400=4(1+2+3+...+100)= \\ \\ =4 \times \frac{100(100+1)}{2} =4 \times \frac{100 \times 101}{2} =4 \times \frac{10100}{2} = \\ \\ =4 \times 5050=20200$