True-False Quiz; Ch 10B

These are just for practice and don't affect your grade. I'm assuming you've read over the text (and especially the thms) in Edwards and Penney, Ch 10. Notation: åan(etc) means "from 1 to ¥"

 

True False. If åan xn converges for x = 2 then it converges for x = -1.

True False. If åan xn converges for x = 2 then it converges for x = -2.

True False. If åan xn converges on (-1,1] then åan (x-1)n converges on (0,2].

True False. If f is even, then its McLaurin series (assume it has one) has only even exponents.

True False. If f is odd then the Taylor series for f at 11 has only odd exponents.

True False. The interval of convergence of åan (x-1)n must be centered at x = 1.

True False. If a power series centered at 0 converges to f(x) on (-1,1), it must be the McLaurin Series of f.

True False. A good test to use on å(-1)k/(k+2) is the Integral Test.

True False. A good test to use on å(k+2)/(k2+1) is the Ratio Test.

True False. A good test to use on å(k+2)/k! is the Ratio Test.

File translated from TEX by TTH, version 3.05. On 11 Mar 2002, 19:36. Written by S Hudson.

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