n² +1 rove that the sequence {an},n=1 converges by following the following sequence of steps. n n=1 0 < a < b, then 0 < va < vb. Use this result to complete the proof.

Q: Use polynomial fitting to find a closed formula for the sequence (an)n 2 1: 4,11, 20, 31, 44,..

A: Given Sentence is 4,11,20,31,44......We can see that       11-4 =7                        }⇒9-7=2…

Q: Use the difference an+1 – an to show that the sequence {n – 11"}t n=1 is strictly increasing or…

A:

Q: a1=1 , an+1=4-an , n is greater than or equal to 1 is the sequence convergent or divergent?  what if…

A: Given that a1=1 and an+1=4-an, n≥1 Write down the first few terms of the sequence: a1=1, Substitute…

Q: Let {n} be a sequence. Let Yn = if {n} is monotonic, 1. Show that n then so is {yn}.

A: What is Monotone Sequence: A sequence can either be constant or monotone. There are two different…

Q: Determine whether the sequence an= 5n+3 Justify your answer. is monotonic. Is it bounded?

A:

Q: Use the difference an+1 – an to show that the sequence {n – 4"to0 is strictly increasing or strictly…

A:

Q: Supposed vn =17-n2  is the explicit specification for a sequence. How many values of n (positive)…

A: Given: Vn=17-n2

Q: (-1)** 3³3n Зп Use the root test to determine if > converges or diverges. 52n+3 n=1

A: Given series is

Q: Determine whether the sequence (3n)/(4n-1) converges or diverges. Show all necessary  calculations…

A: Given an=3n4n-1

Q: The sequence (c} diverges.

A: To check whether the sequence diverges

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.