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 1 a 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 (n 2 3) (4n 2 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 1 a 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

Question: 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

1. Let a_n=6(0.7)^(n-1) - (0.5)ⁿ

(a) Find the lim_n>infa_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>infa_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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