Find the sum of the infinite series $$\(\sum_{n=0}^{\infty} \frac{(-1)^{n} 2^{n}}{3^{n} n!}\)$$.

A.
\(e^{3 / 2}\)
B.
3
C.
\(-e^{3 / 2}\)
D.
\(e^{-2 / 3}\)
Calculus
AP
College Board
Exam No:AP Calculus Unit 10 Questions Set 2 Year:2024 Question No:39

Answer:

D

Knowledge points:

10.15 Representing Functions as Power Series
10.2 Working with Geometric Series

Solution:

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