Question

(a) Use differentiation to find a power series representation for

Answer 1

Answer:1/(3+x)=(1/3)

1

(1−(−x/3))

1/(3+x)=(1/3)1(1−(−x/3))

Use this fact that  

1/(1−t)=

∑

∞

0

t

n

  (∗)

1/(1−t)=∑0∞tn   (∗)

where  

|t|<1

|t|<1

. I mean take  

t=−x/3

t=−x/3

and...

Note that  

|−t|=|t|<1

|−t|=|t|<1

is the radius of convergence

Step-by-step explanation: