16.131
1+3+5+7 + ......... ....................+19 + 22 + 24+ 26 +.....................+40
41 + 43 + 45 +.........................+59 + 62 + 64 + 66 +....................+80
..................................................................................................................
361 +363 + 365 +...................+379 + 382 + 384+...........................+400
1 +3 + 5 +.....+19 = 1+2 +3 +4.....+19 -(2+4 +........18) =
= 19·20/2 - 2(1+2 +3 +.....+9) = 190 - 90 =100 =S1impar
22+24 +...+40 = (20+2)+(20+4)+..+(20 +20) = 20·10 +2·10·11/2 =310 =S1par
41 + 43 +..+ 59 = 40·10 +S1impar = 500 62 +64+..+80 = 400+S1par = 710
...................................................................................................................
361 +363+...+449 =3600 +100 =3700 382 +....+400 = 3600+ 310 = 3910
S=(100+500+900+..+3700) +(3910+3510 +....+710+310) = 4010·10 = 40100
16. 133
n = (x+9)/(x+1) x = a (a+9)/(a+1) ∈N ⇔ (a+1)∈D(a+9)
(a+1) | (a+1) (1)
(a+1) | (a+9) (2) ⇒ (a+1) | [(2) - (1)] = 8 ⇒ (a+1) ∈ D8
(a+1) ∈ {1,2,4,8} a ∈ {0,1,3,7}
16,132.
initial: M
dupa prima sortare au ramas 92% ·M = 0,92M
dupa a 2-a sortare au ramas 96%·0,92M =44160 ⇒
⇒ M = 44160/(0,92·0,96) = 50000kg
