Final answer:
To find a formula for the sum of the series, rewrite each term as a geometric series and use the formula S = a/(1-r).
Step-by-step explanation:
The given series is ∑_{n=0}^{[infinity]} (((n + 1)x^n) / (11^(n + 2)))
To find a formula for the sum of this series, we can rewrite each term as a geometric series. The sum of a geometric series is given by S = a/(1-r), where a is the first term and r is the common ratio.
In this case, the first term is ((n + 1)x^n) / (11^(n + 2)) and the common ratio is x/11.
Therefore, the sum of the series is S = ((n + 1)x^n) / (11^(n + 2)(1 - (x/11))).