121616949-math.287

# 121616949-math.287 - as appropriate 25 2 x β 26 ln(1 x...

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10.12 Additional exercises 273 Find the interval and radius of convergence; you need not check the endpoints of the intervals. 18. X n =0 2 n n ! x n 19. X n =0 x n 1 + 3 n 20. X n =1 x n n 3 n 21. x + 1 2 x 3 3 + 1 · 3 2 · 4 x 5 5 + 1 · 3 · 5 2 · 4 · 6 x 7 7 + · · · 22. X n =1 n ! n 2 x n 23. X n =1 ( - 1) n n 2 3 n x 2 n 24. X n =0 ( x - 1) n n ! Find a series for each function, using the formula for Maclaurin series and algebraic manipulation
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Unformatted text preview: as appropriate. 25. 2 x β 26. ln(1 + x ) β 27. ln β 1 + x 1-x Β« β 28. β 1 + x β 29. 1 1 + x 2 β 30. arctan( x ) β 31. Use the answer to the previous problem to discover a series for a well-known mathematical constant. β...
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