Question

Va rog daca puteti poza,
dau coroana.
​

Answer 1

$8^{4p}=\mathcal{M}_{10}+6.\\8^{4p+1}=\mathcal{M}_{10}+8.\\8^{4p+2}=\mathcal{M}_{10}+4.\\8^{4p+3}=\mathcal{M}_{10}+2.\\-----------\\grupam~termenii~sumei~S=8^1+8^2+8^3+...+8^{2020},~cate~4.\\S=(8+8^2+8^3+8^4)+(8^5+8^6+8^7+8^8)+...+(8^{2017}+8^{2018}+8^{2019}+8^{2020}).\\S=\underbrace{(\mathcal{M}_{10}+(6+8+4+2))+(\mathcal{M}_{10}+(6+8+4+2))+...+(\mathcal{M}_{10}+(6+8+4+2))}_{de~2020~ori}.\\S=\underbrace{(\mathcal{M}_{10}+20)+(\mathcal{M}_{10}+20)+...+(\mathcal{M}_{10}+20)}_{de~2020~ori}.$$S=\underbrace{\mathcal{M}_{10}+\mathcal{M}_{10}+...+\mathcal{M}_{10}}_{de~2020~ori} =\mathcal{M}_{10}.$