An=(sin^4)(n)/LNn find the sum of the sequence please show work Solution MATH 14

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An=(sin^4)(n)/LNn find the sum of the sequence please show work

Explanation / Answer

MATH 141 EXAM II SAMPLE B 1. Evaluate the lim x!1 x 3 x 2 + x 1 2x3 x2 x : a) 2 3 b) 1 2 c) 2 5 d) 1 e) 0 2. Evaluate the lim x!0 e 2x 1 2x3 : a) +1 b) 1 c) 0 d) e 2 2 e) cannot be determined 3. Evaluate the lim x!0+ ln(sin(3x)) ln(tan(3x)) : a) 3 b) 0 c) 3 d) 1 e) 1 4. Evaluate Z 1 1 2dx x2 : a) 0 b) 2 c) 2 d) 4 e) does not exist 5. Which one of the following is true for the integral Z 1 2 1 (x 1) p dx? a) Diverges for p = 1 and converges for both p > 1 and p < 1: b) Converges for p 1 and diverges for p > 1: c) Converges for p > 1 and diverges for p 1: d) Converges for p 1 and diverges for p < 1: e) Converges for p < 1 and diverges for p 1: 6. Find the limit of the sequence an = (1) n (ln(n)) 2 n . a) 1 b) e 2 c) 1 d) 0 e) +1 7. Find the sum of the following series: X1 n=1 (3) n1 4n : a) 1 7 b) 1 7 c) 7 4 d) 7 4 e) 7 8. For which values of p is does the following series converge? X1 n=2 1 n(ln(n)) p7 a) p 8 b) p > 8 c) p > 7 d) p < 7 e) p 7 1

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