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Question

# Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of partial sums on the same screen. Does it appear that the series is convergent or divergent? If it is convergent, find the sum. If it is divergent, explain why. $\sum_{n=1}^{\infty}(0.6)^{n-1}$

Solution

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From the photo, we can see that the sequence of terms (orange) converges towards 0 while the sequence of partial sums (black) converges towards $2.5$. Therefore, it appears that the series is convergent. Let's find the sum.

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