- #1
geomajor
- 10
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1. Express the function as the sum of a power series by first using partial fractions. Find the interval of convergence.
f(x)= (7x-1)/(3x^2 +2x-1)
2. using the fact that 1/(1-x) =[tex]\sum[/tex] from [tex]\infty[/tex] to n=0 of x^n and the interval for convergence of that is (-1,1)
3. I know that (7x-1)/(3x^2 +2x-1) can be factored to (7x-1)/(3x-1)*1/(1+x).
So, using the idea of partial fractions and the method for changing functions into power series, 1/(1+x) would become 1/(1-(-x)).
Let u=-x so that [tex]\sum[/tex] from infinity to n=0 is (-1)^n*x^n , interval of convergence is (-1,1).
But I know don't know how to do (7x-1)/(3x-1). Is there some way to rewrite that? Like (1-7x)/(1-3x), but I still wouldn't know what to substitute...(-7/3)x? At the end I would have the sum of two series, right?? Help...
f(x)= (7x-1)/(3x^2 +2x-1)
2. using the fact that 1/(1-x) =[tex]\sum[/tex] from [tex]\infty[/tex] to n=0 of x^n and the interval for convergence of that is (-1,1)
3. I know that (7x-1)/(3x^2 +2x-1) can be factored to (7x-1)/(3x-1)*1/(1+x).
So, using the idea of partial fractions and the method for changing functions into power series, 1/(1+x) would become 1/(1-(-x)).
Let u=-x so that [tex]\sum[/tex] from infinity to n=0 is (-1)^n*x^n , interval of convergence is (-1,1).
But I know don't know how to do (7x-1)/(3x-1). Is there some way to rewrite that? Like (1-7x)/(1-3x), but I still wouldn't know what to substitute...(-7/3)x? At the end I would have the sum of two series, right?? Help...