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Practice Midterm 1

# Practice Midterm 1 - Hint 1-1 n 2 = n 2-1 n 2 = n-1 n 1 n Â...

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Math 127 - Spring 2008 Practice for First Examination 1. Calculate the following limit if it exists. lim n →∞ e 2 n + n 5 e 5 n n 4 (3 ne 2 n + 1)(4 e 3 n + 5 n ) . 2. Determine whether the series X n =1 1 + ln( n ) n e - (1+ln( n )) 2 is convergent or divergent. Justify your answer. 3. Calculate the following limit if it exists. lim n →∞ e (2 /n ) - n 2 . 4. Decide whether the series X n =1 ln 1 - 1 n 2 converges or diverges. If it converges, calculate the limit exactly. If it diverges, explain why.
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Unformatted text preview: ( Hint: 1-1 n 2 = n 2-1 n 2 = ( n-1)( n +1) n Â· n and ln( ab ) = ln a + ln b . ) 5. Does the series âˆž X j =1 (-1) n n ln( n ) converge or diverge? 6. Find a number N such that âˆž X n =1 n 2 e n 3 !-N X n =1 n 2 e n 3 ! < 10-6 . 1...
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