Question: 4. (10 points) Using the known Taylor series for er er = 1+It 21 + 3! + 1 + ...= for all I n= 0

4. (10 points) Using the known Taylor series for er er = 1+It 21 + 3! + 1 + ...= for all I n= 0 answer the following: (a) (3 pts) Find the power series representation of f(t) = te". What is its radius of conver- gence? where up o not in (b) (4 pts) Find the power series representation of tell at. (c) (3 pts) Use your answer to part (b) to find the sum of the following series: 1 1 1 1 2 + 4 6. 21 8. 3! 1 +

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