Question

Determinati ultima cifra a numarului :
C=3la 0+3la1+3la2+3la3+...3la42 la=la putere

Answer 1

C=1+3+3²+3³+...+3⁴²/·3
3C=3+3²+3³+3⁴+...+3⁴³
3C-C=3⁴³-1
2C=3⁴³-1
C=[3⁴³-1]/2⇒U,C[3⁴³]=U.C[3³]=U.C[27]=U.C[7]=7;
⇒U.C[7-1]/2=U.C[6/2]=U.C[3]⇒ultima cifra a numarului este 3;