Please explain your steps and answer all parts!

a)

Determine the interval of convergence of the infinite series (n + 6)! 1. converges only atr = 0 2, interval convergence = (-6, 6) g. interval convergence = [-6, 6] 4, interval convergence = (-1, 1] 5, interval convergence = (-00, oo) 6. interval convergence = [-1, 1]If the series is convergent, which of the following state- ments must be true without further restric tions on ca? 1. E . (-3)" is convergent 2. (-9)" is divergent THE= 0 3. " (-9)" is convergent 4. E n ( 3)" is divergent 0Find a power series representation for the function 9t + 1' 1. f(t) = 2. f (() = 3. f(t) = 4. f(t) = 5. f (t) = 6. f(t) =