Question

Determinati ultima cifra a numerelor:
b) b= 7+(7 la puterea 2) +(7 la puterea 3) +...+(7 la puterea 43)
c) c= (3 la puterea 0) +3 +(3 la puterea 2) +(3 la puterea 3 )+...+(3 la puterea 4)
d) d= 8+ (8 la puterea 2) +(8 la puterea 3) +...+(8 la puterea 88).

Ma puteti ajuta???
Multumesc!!!!

Answer 1

b= (7+7²+7³+7^4) + 7^5 (7+7²+7³+7^4) + 7^10n (7+7²+7³+7^4) +.................. 7^35 (7+7²+7³+7^4) + 7^40 (7+7²+7³)

Uc(7+7²+7³+7^4) =Uc(7+9 +3+1)=0⇒Uc(b) = 0+0+0+..+ Uc[7^40(7+7²+7³)] = Uc( 1+7+9+3)= 0 ⇒  Uc(b) =0     observatie:  Uc(7^4k) =1

c= 1 +3+3²+3³+3^4      Uc(c) =Uc(1+3+9+7+1) = 1    Uc(c) = 1

d)     8^1 = 8    8²=64   8³=512     8^4 = ....6 ⇒      Uc(8+8²+8³+8^4) =0    ⇒  d = (8+8²+8³+8^4) + 8^5 (8+8²+8³+8^4) + ...........+8^84 (8+8²+8³+8^4)⇒  Uc(d) =0