Infiniti

Ok, i am doing an ap calc bc free response. the question islet f be the function defined by f(x) = sum of the terms to infiniti, with n =1 of ((x^n)(n^n))/((3^n)(n!))a)find the radius of convergence of this seriesb)use the first 3 terms of htis series to find an apporximation of f(-1)c)estimate the amount of error involved in the approxmiation in part b. justify your answerthanks

♠ t=x/3; f(t) =t +(2t)^2/2! +(3t)^3/3! +++ (nt)^n /n! +++♣ u[n] = n^n *t^n /n!; u[n+1]= (n+1)^(n+1) *t^(n+1) /(n+1)!; u[n+1]/u[n] = (1+1/n)^n *(n+1) *t /(n+1) = t*(1+1/n)^n == {for n→ ∞} = t*e; d’alamber says t*e _1 for convergence!♦ thus t _ 1/e; or |x| _ 3/e is radius!