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STD 11 - 7. binomial theoram — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 7. binomial theoram4 Marks
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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