# 3rd - f x = x 4 x 1 5 Evaluate the indeﬁnite integral as...

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MATH 120 RECITATION QUESTIONS WEEK 3 1. Find the radius of convergence and interval of convergence of the series. a ) X n =1 x n 5 n n 5 b ) X n =2 x n (ln n ) n 2. A function f is deﬁned by f ( x ) = 1 + 2 x + x 2 + 2 x 3 + x 4 + ··· that is, its coeﬃcients are c 2 n = 1 and c 2 n +1 = 2 for all n 0. Find the interval of convergence of the series and ﬁnd an explicit formula for f ( x ). 3. Show that if lim n →∞ n p | c n | = c , where c 6 = 0, then the radius of convergence of the power series c n x n is R = 1 /c . 4. Find a power series representation for the function and determine the interval of convergence.
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Unformatted text preview: f ( x ) = x 4 x + 1 5. Evaluate the indeﬁnite integral as a power series.What is the radius of convergence? Z arctan( x 2 ) dx 6. a ) Show that the function f ( x ) = ∞ X n =0 x n n ! is a solution of the diﬀerential equation f ( x ) = f ( x ) b ) Show that f ( x ) = e x . 7. Find the sum of each of the following series. a ) ∞ X n =2 n ( n-1) x n , | x | < 1 b ) ∞ X n =2 n 2-n 2 n c ) ∞ X n =1 n 2 2 n 1...
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