Giải:
a)
\(S=2+2^2+2^3+...+2^{20}\)
\(\Leftrightarrow2S=2\left(2+2^2+2^3+...+2^{20}\right)\)
\(\Leftrightarrow2S=2^2+2^3+2^4+...+2^{21}\)
\(\Leftrightarrow2S-S=2^{21}-2\)
\(\Leftrightarrow S=2^{21}-2\)
Vậy ...
b)
\(B=3+3^3+3^5+...+3^{21}\)
\(\Leftrightarrow3^2B=3^2\left(3+3^3+3^5+...+3^{21}\right)\)
\(\Leftrightarrow9B=3^3+3^5+3^7+...+3^{23}\)
\(\Leftrightarrow9B-B=3^{23}-3\)
\(\Leftrightarrow8B=3^{23}-3\)
\(\Leftrightarrow B=\dfrac{3^{23}-3}{8}\)
Vậy ...
