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8.6.4. Determine the radius and interval of convergence.k-0 to inf,(a)2)Or sqrt(x 2)-2to 2Therefore converges when x2So the radius is 2

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8.6.4.   Determine the radius and interval of convergence.

Sum from k=0 to inf, ((k)/(2^k)(x^k)

Or sqrt(x^2)

-2 to 2

Therefore converges when |x|<2

So the radius is 2

8.6.4. Determine the radius and interval of convergence.
k-0 to inf,(a)2)
Or sqrt(x 2)
-2to 2
Therefore converges when x2
So the radius is 2
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8.6.4. Determine the radius and interval of convergence. k-0 to inf,(a)2) Or sqrt(x 2) -2to 2 Therefore converges when x2 So the radius is 2

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Step 1

Firstly, we find the radius of convergence as shown on board.

Therefore, series is convergent for every x between -2 to 2.

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Step 2

At x=-2, series is oscillting and hence not convergent

At x=2, series is divergent as its  sequence of parti...

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