(4 marks) Consider the infinite series 00 n=1 where on = n! a) Use the ratio test to prove that the series converges. First, write an expression for non/(4*(n+1 )"n) Next, compute the limit On+1 lim 1/(4*exp(1)) G (Write the exact value in Maple syntax) Hence, explain in a short sentence why this implies that the series converges: Note the question continues below the essay box. A - A - IX BIUS X X Paragraph if the limit of the series is less than 1 the series converge; because the limit in this series is 1/(4*exp(1)) = 1. the series of a(n+1)/a(n) converges.b) Using a), explain in words why lim an = 0 (you can type a(n) for an ). Note the question continues below the essay box. 20 X A - A- IX BIUS X X Paragraph 714 Because from a) we know that the G body p Words: 7 36 XEMRT: 18:42:47 c) Hence, explain why there exists M > 0 with the property that if a > M then 4"," > 10(!). A - A -I BI US X X