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Practice Final II for MATH 72

Practice Final II for MATH 72 - San Jos City College...

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San José City College Mathematics 72 Practice Exercises for the Final Examination 1. Determine whether the series 9 8 2 3 2 5 ! k k k + = converges or diverges. Explain your reasoning. 2. Determine whether the series 1 1 sin n n = converges or diverges. Explain your reasoning. 3. Determine whether the series 3 1 1 4 5 n n n = + + converges or diverges. Explain your reasoning. 4. Let and 1 1 a = 1 sin( ) n n n a a n + = 1 n , for . Use the Ratio Test to show that converges. 1 n n a = 5. Determine whether the series 5 1 5 n n n = converges or diverges. Explain your reasoning. 6. Using the Taylor series for ( ) x f x e = , obtain a power series representation for 3 ( ) x g x xe = and for 1 ( ) 1 x h x e x = . 7. Find the sum of the following series: 5 7 8 1 2 k k k + = .

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