- #1
popo902
- 60
- 0
Homework Statement
Determine the an so that the equation
[itex]\sum_{n=1}^{\infty}{na_{n}x^{n-1}} + 2\sum_{n=0}^{\infty}{a_{n}x^{n}} = 0
[/itex]
is satisfied. Try to identify the function represented by the series
[itex]\sum_{n=0}^{\infty}{a_{n}x^{n}} = 0
[/itex]
Homework Equations
The Attempt at a Solution
what i have so far is
[itex]\sum_{n=0}^{\infty}x^{n}[{a_{n+1}(n+1) + 2a_{n}}]= 0
[/itex]
i just combined the series.
then i solved for a,n
an = -1/2(an+1)(n+1)
so...is this right?
if it is, where do i go from here?