What is the interval of convergence of #sum {(x - 7)^n}/{(7)^n}#?
1 Answer
Nov 16, 2015
The interval of convergence for
Explanation:
The ratio test states that a series
- Converges if
#0 <= lim_(n->oo)|a_(n+1)/a_n| < 1# - Diverges if
#lim_(n->oo)|a_(n+1)/a_n| > 1# - May or may not converge if
#lim_(n->oo)|a_(n+1)/a_n| = 1#
We are looking for the interval on which
So we know that the interval of convergence includes
At
At
Thus the interval of convergence for