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Geometric Sequenceseasy
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Which of the following infinite geometric series converge?

I. ∑n=1∞3⋅(1.5)n−1\sum_{n=1}^{\infty} 3 \cdot (1.5)^{n-1}∑n=1∞​3⋅(1.5)n−1 II. ∑n=1∞2⋅(−0.3)n−1\sum_{n=1}^{\infty} 2 \cdot (-0.3)^{n-1}∑n=1∞​2⋅(−0.3)n−1 III. ∑n=1∞5⋅(1)n−1\sum_{n=1}^{\infty} 5 \cdot (1)^{n-1}∑n=1∞​5⋅(1)n−1