Let a > 1. (a) Show that a" > n(a – 1) for all n > 1. [Hint: Write a = 1+b, where b > 0, and use the Binomial Theorem. ] (b) Use the above to prove that lim - no a" = 0. (c) Deduce using l'Hôpital's rule that lim no a" = 0. (Note: by the definition of a sequence, you cannot differentiate a sequence.)

Let a > 1. (a) Show that a" > n(a – 1) for all n > 1. [Hint: Write a = 1+b, where b > 0, and use the Binomial Theorem. ] (b) Use the above to prove that lim - no a" = 0. (c) Deduce using l'Hôpital's rule that lim no a" = 0. (Note: by the definition of a sequence, you cannot differentiate a sequence.)

Name: Let a > 1.(a) Show that a" > n(a – 1) for all n > 1. [Hint: Write a =
Uploaded: 2024-03-20T06:38:58.000Z
Channel: Bartleby
Description: Let a > 1.(a) Show that a" > n(a – 1) for all n > 1. [Hint: Write a = 1+b, where b > 0, and use the Binomial Theorem. ](b) Use the above to prove that lim -no a"= 0.(c) Deduce using l'Hôpital's rule that limno a"= 0. (Note: by the definition of a se