a) \(B=3+3^2+...+3^{90}\)
\(\Leftrightarrow B=\left(3+3^2\right)+...+\left(3^{89}+3^{90}\right)\)
\(\Leftrightarrow B=\left(3+3^2\right)+...+3^{88}.\left(3+3^2\right)\)
\(\Leftrightarrow B=12+...+3^{88}.12\)
\(\Leftrightarrow B=12.\left(1+...+3^{88}\right)⋮4\left(đpcm\right)\)
b)\(B=3+3^2+...+3^{90}\)
\(\Leftrightarrow B=\left(3+3^2\right)+...+\left(3^{89}+3^{90}\right)\)
\(\Leftrightarrow B=\left(3+3^2\right)+...+3^{88}.\left(3+3^2\right)\)
\(\Leftrightarrow B=12+...+3^{88}.12\)
\(\Leftrightarrow B=12.\left(1+...+3^{88}\right)⋮12\left(đpcm\right)\)
c) \(B=3+3^2+...+3^{90}\)
\(\Leftrightarrow B=\left(3+3^2+3^3\right)+...+\left(3^{88}+3^{89}+3^{90}\right)\)
\(\Leftrightarrow B=\left(3+3^2+3^3\right)+...+3^{87}.\left(3+3^2+3^3\right)\)
\(\Leftrightarrow B=39+...+3^{87}.39\)
\(\Leftrightarrow B=39.\left(1+..+3^{87}\right)⋮39\left(đpcm\right)\)
