state gov DSSSB Patwari Mock Test Mathematics Limit and Continuity Evaluation of Limits

If for t ≥ 0 a random variable X with limit \(P(X=t)=\dfrac{(t+1)a}{3^t}\) is {0, 1, 2, 3 ....}, then find the value of \(\dfrac{1}{a}\).

1
\(\dfrac{2}{3}\)
2
\(\dfrac{16}{81}\)
3
\(\dfrac{8}{27}\)
4
\(\dfrac{9}{4}\)
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