Consider the series (n=1 and infinite) ∑(−1)^(n+1) (x−3)^n / [(5^n)(n^p)], where p is a constant and p > 0.
a) For p=3 and x=8, does the series converge absolutely, converge conditionally, or diverge? Explain your reasoning.
b) For p=1 and x=8, does the series converge absolutely, converge conditionally, or diverge? Explain your reasoning.
c) When x=−2, for what values of p does the series converge? Explain your reasoning.
(d) When p=1 and x=3.1, the series converges to a value SS. Use the first two terms of the series to approximate S. Use the alternating series error bound to show that this approximation differs from S by less than (1/300,000).
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Consider the series (n=1 and infinite) ∑(−1)^(n+1) (x−3)^n / [(5^n)(n^p)], where p is a constant and...
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