Question

22 Determinați ultima cifră a numărului:

a) x = 2015 ^ 2019 + 2016 ^ 2019 + 2017 ^ 2019 + 2018 ^ 2019=

b) x = 0 ^ 2 + 2 ^ 1 + 2 ^ 2 + 2 ^ 3 + ... + 2 ^ 2019 + 2 ^ 2020=

c) x = 2017 ^ 2017 + 2018 ^ 2018 + 2019 ^ 2019 + 2020 ^ 2020=

Dau coroana​

Answer 1

Răspuns:

a) U(x)=U(5^9+6^9+7^9+8^9)=U(1953125+10077696+40353607+134217728)=U(5+6+7+8)=U(26)=U(6)

b) U(x)=U(0^2+2^1+2^2+2^3+...+2^2019+2^2020)=U(0+2+4+8+...+4076361+4080400)=U(4080400*(4080400+1)/2)=U(4080400*4080401/2)=U(16649668240400/2)=U(0)

c) U(x)=U(2017^2017+2018^2018+2019^2019+2020^2020)=U(7^7+8^8+9^9+0^0)=U(823543+16777216+387420489+0)=U(3+6+9)=U(18)

Sper că te-am ajutat! ^^