Find the power series for f(x)= 1/(5-x). I have (1/5) SUM (x/5)^ n. Can't I just leave it in this form? Do i have to make it SUM [(x^n/5^n+1)]??

Question

Find the power series for f(x)= 1/(5-x).  I have (1/5) SUM (x/5)^ n.    Can't I just leave it in this form? Do i have to make it SUM [(x^n/5^n+1)]??

amistre64 · Answer

do long division on it; it creates a power series for it

amistre64 · Answer

1/5+x/5^2+x^2/5^3 ....
      ---------------------
5-x ) 1
       (1-x/5)
       --------
            x/5
           (x/5 - x^2/5^2)
          -------------
                    x^2/5^2

$$\sum_{n=0}^{inf}\frac{x^n}{5^{n+1}}$$

amistre64 · Answer

you can factor out the 1/5 yes

amistre64 · Answer

im not sure what a simplified form of summations would be tho :)  quite frankly, i find simplifications to be duplicitous at best

anonymous · Answer

It makes the sum look nicer........and thats all. Im not that good at this, so I want to make things as simple as possible.

amistre64 · Answer

remember what a summation is :

sum can = ca1 + ca2 + ca3 + ca4 ...

we can factor out the c (constant)

c sum an = c (a1 + a2 + a3 + a4 ...)

anonymous · Answer

True. Im leaving it as is then!! Muah ha ha. Thanks....again!

amistre64 · Answer

yw :)