mathmatics analysis   For a convergent real sequence sn and a real number a, show that if sn ≥ a for all but finitely many values of n, then limn→∞ sn ≥ a

Q: Find the generating function for the finite sequence 2, 2,2, 2, 2, 2.

A: Step 1: Consider the provided question, Given, the finite sequence 2, 2, 2, 2, 2, 2.

Q: (-1)"n en

A:

Q: Let {bn} be a sequence whose limit is 3. Show that if B is an upper bound of this sequence, then 3 <…

A: We will use the definition of limit.

Q: a) Sn b) Sn || 1 - 2n n+1 n +3.(-1)" 3n-1

A: Answer given below.

Q: whether the statement is true or false. a) Sequence is convergent if and only if monotone.

A: False

Q: A divergent sequence is a Cauchy sequence. ylgn ihi

A: False

Q: (b) Consider a sequence defined by £₁ = 1, n+1 = 2+1. Prove that the sequence converges and In find…

A:

Q: Find ai for the sequence with generating function, 1-x 1 x x

A: Simplify the generating function.

Q: vīz, vi2+ V12 , V12+ V12+ V12 ,. .... Consider this sequence: i.e., a, = V12, a,1 = V12+a, ,n>1 Use…

A: Given a1=12 and an+1=12+an, n&gt;1 First of all, we will write the first 10 terms in the given…

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

A: Given an=3n4n-1

Q: Σ N 3 | n² 3 2 (n + 1)²

A:

Q: Limit calculations. For each real-valued sequence, explain whether it is convergent, divergent to…

A:

Q: Decide whether or not the infinite sequence is a cauchy sequence. If it is not a cauchy sequence,…

A: The infinite sequence is .To Find:Determine whether it is a Cauchy sequence or not.

Q: n=0 Let An be a sequence so that lim an/√n = 0. Show that the series neoo converges.

A: Given: Let an is convergent and limn→∞ an/n=0 . To Show :∑n=0n=∞ann2 is convergent .