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Confergence of series

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1.) Find the interval of convergence of the series Σ (for n=0 to ∞) (4x-3)^(3n)/8^n and, within this interval, the sum of the series as a function of x.

2.) Determine all values for which the series Σ (for n=1 to ∞) (2^n(sin^n(x))/n^2 converges.

3.) Find the interval of convergence of the series Σ (for n=1 to ∞) (3^n (x-2)^n)/((the square root of (n+2)) 2^n)

4.) Suppose the interval of convergence of the Maclaurin series for f(x) is -2 < x < 2.
If the Maclaurin series for (the integral from 0 to x) f(t) dt is obtained by integrating
term-by-term, which of the following could be the interval of convergence of new
series?
I. -2 < x < 2 III. -2 &#8804; x < 2
II. -2 < x &#8804; 2 IV. -2 &#8804; x &#8804; 2
a.) I only c.) II and III e.) I, II, III, IV
b.) IV only d.) I, II, III

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Solution Summary

This is a set of questions regarding convergence of series. The intervals of convergence of series are determined.

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