Cái này tag tên tú hay ace cũng được mà:
Đặt+ sưả đề:
\(A=1+2+2^2+2^3+-.+2^{2004}+2^{2005}\)
\(2A=2\left(1+2+2^2+2^3+-.+2^{2004}+2^{2005}\right)\)
\(2A=2+2^2+2^3+2^4+-.+2^{2005}+2^{2006}\)
\(2A-A=\left(2+2^2+2^3+2^4+-.+2^{2005}+2^{2006}\right)-\left(1+2+2^2+2^3+-.+2^{2004}+2^{2005}\right)\)\(A=2^{2006}-1\)
Tìm chữ số tận cùng:
a;b dễ tự làm nha
c) \(19^n+5n+1890^n\)
Xét:
n lẻ:
\(\Rightarrow19^n=\overline{-9}\)
\(\Rightarrow5n=\overline{-5}\)
\(\Rightarrow1980^n=\overline{-0}\)
\(\Leftrightarrow19^n+5n+1980^n=\overline{...9}+\overline{...5}+\overline{...0}=\overline{...4}\)
Xét: n chẵn:
\(\Rightarrow19^n=\overline{-1}\)
\(\Rightarrow5n=\overline{...0}\)
\(\Rightarrow1890^n=\overline{...0}\)
\(\Leftrightarrow19^n+5n+1980^n=\overline{...1}+\overline{...0}+\overline{...0}=\overline{...1}\)
\(2^{4n}+1\)
\(4n⋮4\)
Nên ta sẽ xét những số mũ chia hết cho 4
\(2^{1.4}=2^4=\overline{...6}\)
\(2^{2.4}=2^8=\overline{...6}\)
\(2^{3.4}=2^{12}=\overline{...6}\)
\(\Rightarrow2^{4n}=\overline{...6}\)
\(\Rightarrow2^{4n}+1=\overline{...7}\)
