In 3n an = In 5n

Q: Which of the sequences whose nth terms appear converge, and which diverge? Find the limit of each…

A: We find the limit of the an th term. limx→∞(an)=limx→∞1+(-1)nn=1+limx→∞(-1)nn=1+0=1

Q: Determine the convergence or divergence of the sequence whose nth term is An=sqrt(n+2)-sqrt(n). If…

A:

Q: A sequence that does not have any convergent subsequence

A: We find a sequence that does not have any convergent subsequence.

Q: Can you further share how to find a convergent sequence

A: Given sequence  by  Here we consider two subsequences .Noted that A sequence  is convergent   are…

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

A: Given an=3n4n-1

Q: Determine if the sequence  {8/1 , 8/3 , 4/2 , 4/4 , 8/5 , 8/7 , 4/6 , 4/8 , . . .}  converges and,…

A: Given, Sequence S=81,83,42,44,85,87,46,48,...

Q: Determine whether the sequence is convergent or divergent. Find the limit of the sequence if it is…

A:

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.