Use a graphing utility to graph the first 10 terms of the sequence with the given nth term. Use the graph to make an inference about the convergence or divergence of the sequence. Verify your inference analytically and, if the sequence converges, find its limit. an = 2 −(1/ 4n )

Decide whether or not the given sequence converges to a limit. If it does not, find, in each case, at least one convergent subsequence. We suppose n= 1, 2, 3,... xn = 1 + ((-1)n/n)

Use a graphing utility to graph the first 10 terms of the sequence with the given nth term. nπ 3 = COS an Use the graph to make an inference about the convergence or divergence of the sequence. The sequence converges. The sequence diverges. Verify your inference analytically and, if the sequence converges, find its limit. (If the quantity diverges, enter DIVERGES.)

Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "oo" (without the quotation marks). If it diverges to negative infinity, state your answer as "-o0". If it diverges without being infinity or negative infinity, state your answer as "DNE". n" lim n+ 00 e4n

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