1. Let a_n=6(0.7)^(n-1) - (0.5)ⁿ

(a) Find the lim_n>inf a_n . Does the sequence {a_n} converge or diverge? Explain why.

(b) Does the series, SUM^inf_n=1a_n converge or diverge? if it converges find the sum SUM^inf_{n=1 .} If it diverges explain why.

(c) Let s_n = SUM^inf_i=1 a_{i .} Does the sequence {s_n} converge or diverge? If it converges, find the limit lim_n>inf s_{n .} if it diverges, explain why.

2. Let a_n= (n²+3)/(4n²+2n)

(a) Find the lim_n>inf a_n . Does the sequence {a_n} converge or diverge? Explain why.

(b) Does the series, SUM^inf_n=1a_n converge or diverge? if it converges find the sum SUM^inf_{n=1 .} If it diverges explain why.

(c) Let s_n = SUM^inf_i=1 a_{i .} Does the sequence {s_n} converge or diverge? If it converges, find the limit lim_n>inf s_{n .} If it diverges, explain why.

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Let an 607n1 05n a To find the limit as n approaches infinity we can observe that as n gets larger the term 05n approaches 0 since it is a decreasing ... View the full answer