Question

The remainder on dividing 1 + 3 + 32 + 33 + … + 32021 by 50 ____ is

Answer 1

The correct answer is 4
$1+3+3^2+....3^{2021}=\frac{3^{2022}-1}{2}$
\frac{1}{2} \left\\{ (10-1)^{1011} - 1 \right\\}
=\frac{1}{2}\left\\{{100k+10110-1-1}\right\\}
$= 50 k_1 +4$
∴ The remainder will be 4.