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| PAGE: 775 | SET: Select | PROBLEM: 1 |
The power series is 
.
Radius of the convergence of the series is 
.
Find the radius of the convergence of 
.
Differentiation and integration of power series.
Theorem 2:
If the power series 
has radius of convergence 
then the function 
is differentiable on the interval 
and
(i) 
, (ii) 
then the radii of the power series in (i) and (ii) are both 
.
Here 
is the derivative of the sum 
.
Therefore by theorem 2, radius of the convergence of is also 
.
Radius of the convergence of is .
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