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Question

lim​n->inf. (-1)n sin(n(n2+5n+1)1/2)

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Solution

Dear student

limn(-1)nsin(nn2+5n+1)(-1)n oscillates between -1 and 1 as n tends to infinity and is finitely bounded whereas in the second term, sin oscillates between -1 and 1so limn(-1)nsin(nn2+5n+1) oscillates between -1 and 1and is undefined

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