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Determine whether the series is convergent or divergent. (-1)(11n) 6n2 - 4 The series ? Justification: (If more than one test is appropriate, pick the
Determine whether the series is convergent or divergent. (-1)"(11n) 6n2 - 4 The series ? Justification: (If more than one test is appropriate, pick the first applicable test in the list.) A. This is a Geometric Series of the form ." n-1 where w - and its sum is (Enter "DNE" if n=1 divergent.) B. This is a Telescoping Series, lim Sn = n-+00 C. By the Divergence Test, lim an = n-+00 D. By the Direct Comparison Test, an c( b ), c = and p = E. By the Direct Comparison Test, an > bn where _ be = E c( m ) where c = and p = OF. By the Limit Comparison Test, let _ br = Ec( m ) where c = P = and lim - an n-100 bn O G. By the Alternating series test, i) {bn } is ultimately decreasing because the function f satisfying f(n) = bn is decreasing on the interval ii) lim bn = n-+00 OH. By the Integral Test, i) The function f satisfying f(n) = an is positive, continuous, and ultimately decreasing on the interval in ( " f(a) da = I. By the Ratio Test, lim an+1 n-+00 an OJ. By the Root Test, limn +0. Van| =
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