Question

Determinați ultima cifra a nr
b=7+7²+7³+...+7⁴³
c=3⁰+3¹+3²+3³+...+3⁴²
d=8+8²+8³+...+8⁸⁸​

Answer 1

b = 7+7²+7³+7⁴+7⁵+...+7⁴³

U(b) = U[(7+9+3+1) + (7+9+3+1) +...+ (7+9+3+1){de 10 ori} + (7+9+3)]

U(b) = U[20+20+...+20 + (7+9+3)]

U(b) = U(0+19)

U(b) = 9

c = 3⁰+3¹+3²+3³+...+3⁴²

U(c) = U[(1+3+9+7) + (1+3+9+7) +...+ (1+3+9+7){de 10 ori) + (1+3+9)]

U(c) = U(20+20+20+...+20 + (1+3+9)]

U(c) = U(0+13)

U(c) = 3

d = 8+8²+8³+...+8⁸⁸​

U(d) = U[(8+4+2+6) + (8+4+2+6) +...+ (8+4+2+6){de 22 ori}]

U(d) = U(20+20+20+...+20)

U(d) = 0