a) Find the values of x for which the given geometric series converges.
b) Find the sum of the series
(a) Consider the given geometric series:
Now, to find the value of x for which the series converges, apply ratio test by finding the following limit:
Now, for the series to be convergent, the limit should be less than 1, that is:
Now, check the convergence at 7 and 3:
At x=7
Which is divergent
At x=3
Which is divergent
Therefore, the required values of x for which the series converges is:
(b) Now, since, given series is a geometric series with:
Therefore, the sum of this infinite series will be given by:
Thus, required sum of series is:
Answer is given below (on video)
How am I supposed to find the solution to the non-homogeneous ode ?