Homework_2.pdf - MATH 102-HOMEWORK 2 Problem 1 Does the series 1 X n=1 converge(Hint Use 1 n 1 n 1 1 n to compare the series Ans Diverges Problem 2

# Homework_2.pdf - MATH 102-HOMEWORK 2 Problem 1 Does the...

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MATH 102-HOMEWORK 2 Problem 1 Does the series 1 X n =1 1 n 1+ 1 n converge? ( Hint: Use 1 n to compare the series) Ans: Diverges Problem 2 Determine whether the series converges or diverges. a) 1 X n =1 ° 1 + 1 n ± 2 e ° n Ans: Converges b) 1 X n =0 1 + sin( n ) 10 n Ans: Converges c) 1 X n =1 e 1 n n 2 Ans: Converges d) 1 X n =1 e 1 n n Ans: Diverges e) 1 X n =1 n 2 e ° n 3 Ans: Converges 1
f) 1 X n =1 1 ( n + 1) ln ( n + 1) Ans: Diverges g) 1 X n =1 sin ° 1 n 2 ± Ans: Converges h) 1 X n =1 1 1 + p n Ans: Diverges Problem 3 Suppose P a n and P b n are series with positive terms and P b n is known to be convergent. a) If a n > b n for all n , what can you say about P a n ? Why? b) If a n < b n for all n , what can you say about P a n ? Why? Problem 4 If P a n is a convergent series with positive terms, is it true that P sin( a n ) is also convergent?

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