How to finish ths last step of the induction question

  • Thread starter transgalactic
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In summary, the conversation is about a question and how to solve the last step. One person suggests using the expression a_n- k(L+ \epsilon)< a_{n+1}< a_n+ k(L+ \epsilon) for k= 1 and then showing that it is also true for k+1. The other person is having trouble applying this step and is looking for further guidance.
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transgalactic
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here is the full question and the last step to which i understand
i don't know how to go further??

http://img147.imageshack.us/img147/3077/14993551of0.gif [Broken]

i got this suggestion from hallsofivy :
You know that for every n, [itex]a_n- L- \epsilon< a_{n+1}< an+ L+ \epsilon[/itex] so [itex]a_n- k(L+ \epsilon)< a_{n+k}< a_n+ k(L+ \epsilon)[/itex] is certainly true for k= 1. Now suppose [itex]a_n- k(L+ \epsilon)< a_n< a_{n+1}+ k(L+ \epsilon)[/itex] is true for some specific k and all n. Then [itex]a_n- (k+1)(L+ \epsilon)= [a_n- (L+ \epsilon)]- k(L+\epsilon)< a_{n+1}-k(L+\epsilon)[/itex] and now use [itex]a_n- k(L+ \epsilon)< a_{n+1}[/itex] with n+1 instead of n- which you can do because it is true for all n.


but i can't see in it my base (k) expression and using it to prove the (k+1) expression
i don't know how to apply it the step i got stuck
??
 
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http://img360.imageshack.us/img360/7791/63228047ot8.gif [Broken]
 
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1. How do I know when I've reached the last step of an induction question?

The last step of an induction question is typically indicated by a specific objective or goal that needs to be achieved. This could be a specific equation or theorem that needs to be proven, or a certain condition that needs to be met. It's important to carefully read the question and identify what the final step entails.

2. What strategies can I use to solve the last step of an induction question?

Some common strategies for solving the last step of an induction question include working backwards, using mathematical induction principles, substituting in values, and breaking the question down into smaller, more manageable parts. It's also helpful to review examples and practice problems to gain a better understanding of the problem-solving process.

3. How can I make sure my solution to the last step of an induction question is correct?

To ensure the accuracy of your solution, it's important to double-check your work and carefully follow each step of the induction process. You can also ask a peer or instructor to review your solution and provide feedback. Additionally, it's helpful to compare your solution to similar problems to see if the steps and reasoning align.

4. What should I do if I get stuck on the last step of an induction question?

If you find yourself stuck on the last step of an induction question, take a step back and review the information and equations given in the question. It may also be helpful to approach the problem from a different angle or try using a different strategy. Don't be afraid to ask for help from a classmate or instructor if you're still having trouble.

5. How can I improve my skills in solving the last step of induction questions?

The best way to improve your skills in solving the last step of induction questions is through practice and repetition. Make sure to review and understand the underlying concepts and principles of mathematical induction. It's also helpful to seek out challenging and diverse practice problems to strengthen your problem-solving abilities.

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