Is this your mid-term quiz? You should be demonstrating SOME knowledge fo the subject. You seem to be just guessing.
I need some help on the following
Determine the interval of convergence of the power series
infinity
sum of series (-1)^n/(n+3)4^n * (x-1)^n
n=1
I have
Here An = (-1)^n/(n+3)4^n, for n=1,2....
1. since
|An+1/An| = 1/(n+4)4^n+1 * (n+3)4^n/1
= ? ----> as n ----> ?
we have R = ? , by the Ratio Test.
Thus
2. If x = ? , the the power series is
?
Hence the interval of convergence is ( ? )
By using d'Alembert test you will come to the same conclusion. We have to calculate (in general):
So in this case:
Along the test the serie wil converge if and diverge if so you've to calculate the values wherefore:
So two different cases:
(1)
(2)