MCQ
$1+2 \cdot 3+3 \cdot 3^{2}+\ldots . .+10 \cdot 3^{9}$ = ...............
- A$\frac{2 \cdot 3^{12}+10}{4}$
- B$\frac{19 \cdot 3^{10}+1}{4}$
- C$5 \cdot 3^{10}-2$
- D$\frac{9 \cdot 3^{10}+1}{2}$
$3 S =1 \cdot 3^{1}+2.3^{2} \ldots \ldots \ldots \ldots \ldots \ldots+9 \times 3^{9}+10 \times 3^{10}$
$-2 S =\left(1 \cdot 3^{0}+3^{1}+3^{2} \ldots 3^{9}\right)-10.3^{10}$
$S =5 \times 3^{10}-\left(\frac{3^{10}-1}{4}\right)$
$S =\frac{20.3^{10}-3^{10}+1}{4}=\frac{19.3^{10}+1}{4}$
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