Determine the radius and interval of convergence of the ff. power series. Show complete solutions and boxyour final answers. (6 pts each) 1. $\sum_{n=0}^{+\infty} \frac{x^n}{n+1}$ 2. $\sum_{n=0}^{+\infty} \frac{x^n}{n^2+3}$ 3. $\sum_{n=0}^{+\infty} \frac{(x+3)^n}{2^n}$ 4. $\sum_{n=1}^{+\infty} \frac{(-1)^{n+1}}{n2^n}(x-2)^n$ 5. $\sum_{n=1}^{+\infty} \frac{(-1)^n}{2^n}(x-6)^n$
Added by Michael S.
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We can rewrite (x-2)^n as (-1)^(n)(2-x)^n. So the power series becomes: ∑ (-1)^(n)(2-x)^n / (2n)^(n^2) Show more…
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