Find the sum of the series summationdisplay n 1 n 2 n

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17. Find the sum of the series summationdisplay n =1 n 2 n - 1 . (a) 1 (b) 2 (c) 3 (d) 4 (e) 5 (f) The series diverges. 18. Consider the polynomial 1 - x 2 2! as an approximation to cos( x ) on the closed interval - 1 x 1. What is the best bound on the error that is given by Taylor’s inequality? 19. What is the general solution of the differential equation dy dx = - xy y 2 + 1 ? What is the behavior of the solutions as x → ∞ ? 20. Which of the following curves is an orthogonal trajectory to the family of curves x 2 4 + y 2 9 = C , where C is an arbitrary positive constant? 3
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