Homework+25+-+Power+Series

# Homework+25+-+Power+Series - 1 )c).Then showthat(a)(b)...

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Homework 25 – Power Series 1) Show that the power series a) – c) have the same radius of convergence. Then show that (a) diverges at both endpoints, (b) converges at one endpoint but diverges at the other, and (c) converges at both endpoints. a) 1 3 n n n x b) 1 3 n n n x n c) 2 1 3 n n n x n 2) Find the radius and interval of convergence. a) 0 n n nx b)  0 3 n n nx c)   0 13 ! nn n x n  d) 0 ! 5 n n n e) 21 15 31 n n x n f) 1 1 2 n n n n x n g)    5 1 17 n  h) 12 2 n n n ex 3) Use 0 1 1 n n x x for 1 x to expand the function in a power series with center 0 c and determine the interval of convergence. a) 1 5 fx x b) 3 1 16 2 x 4) a) Use differentiation to show that

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Homework+25+-+Power+Series - 1 )c).Then showthat(a)(b)...

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