\(S=2^1+2^2+2^3+...+2^{100}\)
\(S=\left(2^1+2^2+2^3+2^4\right)+...+\left(2^{97}+2^{98}+2^{99}+2^{100}\right)\)
\(S=2\left(1+2+2^2+2^3\right)+...+2^{97}\left(1+2+2^2+2^3\right)\)
\(S=\left(2+...+2^{97}\right)\left(1+2+2^2+2^3\right)\)
\(S=Q.15\)
\(S=Q.3.5\)
\(\Rightarrow S⋮5\) (1)
\(S=2^1+2^2+2^3+...+2^{100}\)
\(S=\left(2^1+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{99}+2^{100}\right)\)
\(S=1\left(2^1+2^2\right)+2^2\left(2^1+2^2\right)+...+2^{97}\left(2^1+2^2\right)\)
\(S=\left(2^1+2^2\right)\left(1+2^2+...+2^{97}\right)\)
\(S=6.Q\)
\(S=2.3.Q\)
\(\Rightarrow S⋮2\) (2)
Từ (1) và (2)
\(\Rightarrow S⋮2;5\)
Vậy \(S\) có tận cùng là 0
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