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# 2JSF1 - FIRST SAMPLE FINAL FOR MATH 2J This sample 2J final...

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FIRST SAMPLE FINAL FOR MATH 2J This sample 2J final exam is meant for practice only. Length and content of the actual final may vary, at the discretion of the instructor. Try to complete the test in 1 hour and 50 minutes, without consulting any book or notes, and without using a calculator. 1

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2 PROBLEM 1 ( True/False Questions ) n =1 ( - 1) n n converges. true false n =1 1 n diverges. true false If n =1 | a n | is divergent, then n =1 a n is divergent. true false If lim n →∞ a n = 0, then n =1 a n is convergent. true false n =0 ( 1 7 ) n = 7 6 . true false n =0 π n = 1 1 - π . true false The ratio test can be used to determine whether n =1 1 n 3 converges. true false
3 PROBLEM 2 Determine whether the sequence is convergent or divergent. If it is convergent, find its limit. a n = n e 2 n diverges converges to: . . . . . . a n = ( - 1) n n ! diverges converges to: . . . . . . a n = ( - 1) n ( 3 + 2 n ) diverges converges to: . . . . . .

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