Determine the radius of convergence of the following power series. then test the endpoints to determine the interval of convergence.

σ(21x)^k

the radius of convergence is r =

a. the interval of convergence is {x: x= }
b. the interval of convergence is:

Radius of the convergence is R =

and,

The Interval of convergence is

Step-by-step explanation:

Given function : Σ(21x)^k

Now,

Using the ratio test, we have

R =

or

R =

or

R =

now,

for convergence R|x| < 1

Therefore,

< 1

or

and,

Radius of the convergence is R =

and,

The Interval of convergence is

d) 30 units^2

area of rectangle = l × b

we know,

length = 10 unit

breadth = 3 unit

applying the formula,

= l × b

= 10 × 3

= 30 unit^2

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