Question

Calculati suma tuturor nr nat de 3 cifre care impartite la 31 dau restul 13.Va rog raspuns repede

Answer 1

$x\to numar \ de \ 3 \ cifre \\\\ x:31=c_1 \ rest \ 13 \\\\ x=M_{31}+13 \\\\\\ 1)x=1*31+13 \\\\ x=31+13 \\\\ x=44-nu \ se \ accepta \\\\\\ 2)x=3*31+13 \\\\ x=93+13 \\\\ \boxed{x=106}-primul \ nr \ de \ 3 \ cifre \ din \ suma \\\\\\ 3)x=4*31+13 \\\\ x=124+13 \\\\ \boxed{137} \\\\\\ 4)x=5*31+13 \\\\ x=155+13 \\\\ \boxed{x=168} \\\\==============\\\\ 32)x=31*31+13 \\\\ x=961+13 \\\\ \boxed{x=974}-ultimul \ nr.\ de \ 3 \ cifre \ din \ suma$

$S=106+137+168+...+974 \\\\ S=\frac{106+974}{2}*31 \\\\ S=\frac{1080}{2}*31 \\\\ S=540*31 \\\\ \boxed{\boxed{S=16740}}$