Question

Ajutătoare va rog!!!.Determinati ultima cifra a numarului n unde: n=1+1la puterea1+2+2la puterea 2+2la puterea3+..........2la puterea2014.va rog aflați numarul!!!!!!:-(

Answer 1

[tex]n=1+2^0+2^1+2^2+....+2^{2014}\\ Luam\ toti\ termeni\ in\ afara\ de\ 1\ si \ ii\ calculam\ separat:\\ a=2^0+2^1+2^2+....+2^{2014}|*(-2)\\ -2a=-2-2^2-...-2^{2015}\\ ........................................+\\ -a=2^0-2^{2015}\\ -a=1-2^{2015}\\ a=2^{2015}-1\\ n=1+a\\ n=1+2^{2015}-1\\ n=2^{2015}\\[/tex]
[tex]2^1=2\\ 2^2=4\\ 2^3=8\\ 2^4=..6\\ 2015:4=503,r=3=\ \textgreater \ n=..8[/tex]