Question

Determinati ultima cifra a nr n unde:n=1+1+2+2 la puterea 2+2 la puterea 3+....+2^2018

Answer 1

n = 1 + 1 + 2 + 2^2 + 2^3 + ...+ 2^2018

notam cu :

a = 1 + 2 + 2^2 + 2^3 + ... + 2^2018

a = 2^0 + 2^1 + 2^2 + 2^3 + ...+ 2^2017 + 2^2018 | × 2

2 × a = 2^1 + 2^2 + 2^3 + 2^4 + ...+ 2^2018 + 2^2019

2×a - a = 2^2019 - 2^0

a = 2^2019 - 1
_____________


n = 1 + a

n = 1 + 2^2019 - 1

n = 2^2019
__________

2019 = 4 × 504 + 3


U( n ) = U( 2^2019) = U ( 2^3) = 8
___________________________

Answer 2

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