Question

A= 1+ 3 +3^2+3^3+3^4

B=(3^2+1). (3^4+1). (3^8+1)

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Answer 1

\(A=1+3+3^2+3^3+3^4\)

\(A=1+3+9+27+81\)

\(A=121\)

\(B=\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\)

\(8B=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\)

\(8B=\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\)

\(8B=\left(3^8-1\right)\left(3^8+1\right)\)

\(8B=3^{16}-1\)

\(B=\frac{1}{8}\left(3^{16}-1\right)\)

\(B=\frac{3^{16}}{8}-\frac{1}{8}\)

\(B=\text{ }\frac{43046721}{8}-\frac{1}{8}\)

\(B=\frac{43046720}{8}\)

\(B=5380840\)