How do you determine whether the sequence #a_n=(2^n+3^n)/(2^n-3^n)# converges, if so how do you find the limit?
1 Answer
Mar 29, 2017
Explanation:
Divide both numerator and denominator by
#lim_(n->oo) a_n = lim_(n->oo) (2^n+3^n)/(2^n-3^n)#
#color(white)(lim_(n->oo) a_n) = lim_(n->oo) ((2/3)^n+1)/((2/3)^n-1)#
#color(white)(lim_(n->oo) a_n) = (0+1)/(0-1)#
#color(white)(lim_(n->oo) a_n) = -1#
