text: Use the ratio test.\nlimit as n goes to infinity of {[(x+6)^(n+1)]/[(n+1)6^(n+1)]}/{[(x+6)^n]/[n*6^n]}\nwhich simplifies to\nlimit as n goes to infinity of [n(x+6)]/[(n+1)*6]\n= (x+6)/6\nSet the absolute value of this to be less than 1\n|(x+6)/6|<1\nThus, the radius of convergence is 6.\nTo find the interval, solve for x\n|(x+6)/6|<1\n-1 < (x+6)/6 < 1  Multiply everything by 6\n-6 < x+6 < 6  Subtract 6 from everything\n-12 < x < 0\nThe endpoints may or may not be included.  They have to be checked.  If you do the check, you will find that it converges at 0 but not -12.  Thus, the interval of convergence is\n(-12,0]