Question

aflați restul împărțirii nr. B=1×2×3×........×20+2020 la 17​

Answer 1

1×2×3×...×20=nr termeni ×(primul+ultimul):2

Nr termeni = (ultimul-primul ): pas+1=(20-1):1+1=19+1=20

1×2×3×...×20=20×(20+1)÷2=20×21÷2=420÷2=210

1×2×3×...×20+2020=210+2020=2230

2230÷17=131 rest 3

Răspuns: restul e 3

Answer 2

Răspuns:

$1.431118828*10^1^7$

Explicație pas cu pas:

$\frac{1*2*3*4*..*20+2020}{17} =\frac{20!+2020}{17} =\frac{(1*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18*19*20)+2020}{17} =\frac{(6*20*42*72*110*156*210*272*342*20)+2020}{17} =\frac{(120*42*7920*32760*272*6840)+2020}{17} =\\=\frac{(5040*259459200*1860480)+2020}{17} =\frac{(5040*4.827186524*10^1^4)+2020}{17} =\frac{(2.432902008*10^1^8)+2020}{17} =\frac{2.432902008*10^1^8}{17}=1.431118828*10^1^7$Succes! :)