Question

2^1+2^2+....2^100 se divide cu 3

Answer 1

[tex]\text{Tinem cont de faptul ca sunt 100 de termeni,deci ii putem grupa}\\ \text{cate doi:}\\ 2+2^2+2^3+\ldots+2^{100}=\\ 2(1+2)+2^3(1+2)+\ldots+2^{99}(1+2)=\\ (1+2)(2+2^3+2^5+\ldots+2^{99})=\\ 3\cdot (2+2^3+2^5+\ldots+2^{99})\ \vdots\ 3[/tex]