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Berkeley
MATH 1B -
Section 107 Quiz
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Math 1B Section 107 Quiz #9Thursday, 25 October 2007GSI: Theo Johnson-Freydhttp://math.berkeley.edu/∼theojfName:1. (3 pts) Write∞Xn=1xn−1n2+ n=12+x6+x212+x320+x430+x542+ . . .in terms of elementary functions. (Hint: Partial fractions) For what values of x isyour solution justified?12. (3 pts) Find the Taylor series expansion of cos(x) centered at c = π/2. What is theinterval of convergence for this series?23. (4 pts) For the following power series(a) find the general nth term (i.e. write it asP∞n=0(something)(b) find the radius of convergence(c) check whether the series converges at the endpointsso that you can determine for which x the series• converges absolutely• converges conditionally• diverges.14+2x9+3x216+4x325+5x436+6x549+ . .
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