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# 1 ) Suppose that a given series Fan , with and O for all n , converges . Which of the following series must converge

1 ) Suppose that a given series Fan , with and O for all n , converges . Which of the following series must converge . Select all that apply . a ) E Isin ( an ) 1 b ) [ I cos ( an) 1 c) Ean d ) 5 Jan hel 2 ) In the following exercises , show and explain your work . ( Apply the limit comparison test ) a ) Calculate the limit lim 1 - cos x " I and use it to find out whether 2 ( 1-cos ( h ) ) converges or diverges . b ) Calculate the limit In ( 1+ x ) x and use it to find out whether Een(ith ) converges or diverges . 3. Consider the series E (c+ " ) ( where c is a constant). For which values of c will the series converge , and for which it diverge ? Justify your answer and show all your work. Iuse the root test for c= $1 , you will need to use a different method )

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