Question

Știind că $1^{2} + 2^{2} + 3^{2}+ ....+ 31^{2} = 10416$, calculați suma S=3+5+8+12+...+467. Mulțumesc anticipat! :*

Answer 1

S =(2+1) +[2+(1+2)] + [2+(1+2+3)] +[2+(1+2+3+4)] +......+[2+(1+2+3+....30)]S = 2×30 + 1 +(1+2) +(1+2+3) +..........+(1+2+3+......30)                              S-60 = S1 = 1+(1+2) +(1+2+3) +..........+(1+2+3+......30)                                1= (1²+1)/2       1+2 = (2²+2)/2       (1+2+3) = (3²+3)/2    (1+2+3+4) =(4²+4)/2 1+2+3+......30 = (30²+30)/2 ⇒ S1 =1/2[(1²+2²+3²+..+30²)+(1+2+3+.....+30)]  ⇒S- 60 =1/2[10416 - 31² +30·31/2] =1/2[9455 + 465]= 1/2×9920 = 4960 ⇒ S=5020