- #1
eibon
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Homework Statement
if {An} converges and lim {An}=L L[tex]\neq[/tex] 0
and {Bn} diverges then does {An X Nn} diverge? prove formally
Homework Equations
The Attempt at a Solution
can anyone give me a hint or show a solution?
eibon said:L<An<L +[tex]\epsilon[/tex] [tex]\leftrightarrow[/tex] [tex]\frac{1}{L +epsilon}[/tex] <[tex]\frac{1}{An}[/tex] < [tex]\frac{1}{L}[/tex]
and M<AnBn<M+ε
then i get [tex]\frac{M}{L+epsilon}[/tex] <Bn< [tex]\frac{M+epsilon}{L}[/tex]
now what do i do?
eibon said:wait how do you get to |Bn-M/L|<e?
eibon said:for the quotient of limits you need both An and Bn to converge to use that, but Bn does not converge so i can't use that. and i don't understand how to get the upper and lower bounds, can you please explain it?
eibon said:ok thanks , just out of curiosity how would you prove it with epsilons
A hard sequence in calculus refers to a sequence of numbers or functions that does not have a clear pattern or formula for calculation. Unlike regular sequences, hard sequences require more complex methods, such as the use of limits and derivatives, to find the value of each term.
To solve a hard sequence question in calculus, you will need to determine the type of sequence (e.g. arithmetic, geometric, etc.) and then apply appropriate techniques, such as finding the limit or using the derivative formula, to find the value of each term. It may also be helpful to look for patterns or clues within the sequence to assist in solving the problem.
No, hard sequence questions usually require the use of calculus techniques such as limits and derivatives to find the solution. Without these methods, it would be difficult to accurately determine the value of each term in the sequence.
One useful tip for solving hard sequence questions in calculus is to try different methods and approaches. It may also be helpful to break the sequence into smaller parts or to look for patterns within the sequence. Additionally, practicing with similar problems can help improve problem-solving skills.
Hard sequence questions are important in calculus because they require critical thinking and the application of advanced techniques. Solving these problems helps to develop problem-solving skills and better understanding of calculus concepts. Additionally, hard sequences can be used to model real-world situations and can be applied in various fields such as physics and engineering.