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**Unformatted text preview: **n =2 (-1) n n (ln( n )) 2 converges. A computer gives the approximate value .84776 to 5 digit accuracy for the sum of this series. Find a specic partial sum which is guaranteed to give this number to 5 digit accuracy. Give evidence supporting your assertion. b) Verify that the innite series n =2 1 n ln( n ) diverges. A computer gives the approximate value of 4.74561 for the 10 , 000 th partial sum. Are the partial 1 sums of this series unbounded? If yes, nd a specic partial sum which is guaranteed to be greater than 100. Give evidence supporting your assertion. Comment In neither case is the best possible partial sum requested. Sup-porting evidence must be presented for the two partial sums given. 2...

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