Question

Determinați ultima cifra a nr.: D)d=8+8^2+8^3+...+8^88

Answer 1

Răspuns:

u(d) =8

Explicație pas cu pas:

$d = 8 + {8}^{2} + {8}^{3} + ... + {8}^{88} \\ d = { {2}^{3} }^{} + ({ {2}^{3} })^{2} + ... + ( { {2}^{3} })^{88} \\ d = {2}^{ 3} + {2}^{6} + {2}^{9} + ... + {2}^{264} \\ d = {2}^{3} (1 + {2}^{2} + {2}^{3} + ... + {2}^{88} ) \\ notam \: s = 1 +2 + {2}^{2} + ... + {2}^{88} \\ 2s = 2 + {2}^{2} + ... {2}^{89} \\ scadem \: 2s - s \: si \: obtinem \\ s = {2}^{89} - 1 \\ u(d) = {2}^{3} \times u(s) \\ u(s) = u( {2}^{89} ) - 1 = > u( {2}^{89} ) = 2 = > u(s) = 1 \\ u(d) = {2}^{3} \times 1 = 8 \times 1 = 8$