JEE Main 2022 · 25 Jun · Shift 2 · Mathematics Q8

MathematicsSingle correct+4 / -1Question 8 of 90

The sum $1+2\cdot3+3\cdot3^2+\dots+10\cdot3^9$ is equal to :

\dfrac{2\cdot3^{12}+10}4

\dfrac{19\cdot3^{10}+1}4

5\cdot3^{10}-2

\dfrac{9\cdot3^{10}+1}2

Answer and worked solution

Official answer: B

Arithmetico-geometric sum. $S=\displaystyle\sum_{k=1}^{10}k3^{k-1}$ ; then $S-3S=\sum_{k=0}^93^k-10\cdot3^{10}=\frac{3^{10}-1}2-10\cdot3^{10}$ .

So $S=\dfrac{19\cdot3^{10}+1}4$ .

(B)

Topics:Arithmetico-geometric series

JEE Main 2022 · 25 Jun · Shift 2, Mathematics question 8