The following series are geometric series or a sum of two geometric series. Determine whether each series converges or not. For the series which converge, enter the sum of the series. For the series which diverges enter "DIV" (without quotes). (a) sum_{n=1}^{infty} frac{11^{n}}{10^{n}} = (b) sum_{n=2}^{infty} frac{1}{2^{n}} = (c) sum_{n=0}^{infty} frac{2^{n}}{5^{2n+1}} = (d) sum_{n=5}^{infty} frac{10^{n}}{11^{n}} = (e) sum_{n=1}^{infty} frac{4^{n}}{4^{n+4}} = (f) sum_{n=1}^{infty} frac{10^{n}+2^{n}}{11^{n}} =
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The series 11" is a geometric series with a common ratio of 11. In order for a geometric series to converge, the absolute value of the common ratio must be less than 1. Since the absolute value of 11 is greater than 1, the series 11" diverges. Show more…
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