Question
Use the formula for the sum of a geometric series to find the sum or state that the series diverges.$$\sum_{n=0}^{\infty} \frac{8+2^{n}}{5^{n}}$$
Step 1
Step 1: First, we can rewrite the given series as the sum of two separate series: $$ \sum_{n=0}^{\infty} \frac{8+2^{n}}{5^{n}} = \sum_{n=0}^{\infty} \frac{8}{5^{n}} + \sum_{n=0}^{\infty} \frac{2^{n}}{5^{n}} $$ Show more…
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