Question

AJUTORRRRRRRRRRRRRRRRRRRRRRRRRRRRRR! CU REZOLVARE. Consideram toate nr.zecimlae periodice simple de forma​

Answer 1

0,(abcd);   0,abcd=abcd/9999

a;b;c;d∈{1;2;3;4}; a≠b≠c≠d

=> abcd∈{1234;1243;1324;1342;1423;1432;  

                  2134;2143;2314;2341;2413;2431;  

                  3124;3142;3214;3241;3412;3421

                  4123;4132;4213;4231;4312;4321}

observam ca fiecare cifra, apare pe fiecare pozitie, (la mii, sute, zeci, unitati), de  6 ori

=> suma =[1000•6(1+2+3+4)+100•6(1+2+3+4)+10•6(1+2+3+4)+6(1+2+3+4)]/9999

=60(1000+100+10+1)/9999

=60•1111/9999

=60/9

=20/3