The remainder on dividing 1+3+3^ 2 +3^ 3 + +3^ 2021 by 50 is - Vidyadip

MCQ

The remainder on dividing $1+3+3^{2}+3^{3}+\ldots+3^{2021}$ by $50$ is

A
$5$
✓
$4$
C
$2$
D
$6$

✓

Answer

Correct option: B.

$4$

b
$\frac{1 .\left(3^{2022}-1\right)}{2}=\frac{9^{1011}-1}{2}$

$=\frac{(10-1)^{1011}-1}{2}$

$=\frac{100 \lambda+10110-1-1}{2}$

$=50 \lambda+\frac{10108}{2}$

$=50 \lambda+5054$

$=50 \lambda+50 \times 101+4$

$\operatorname{Rem}(50)=4 .$

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