# How to finish ths last step of the induction question

1. Jan 6, 2009

### transgalactic

here is the full question and the last step to which i understand
i dont 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, $a_n- L- \epsilon< a_{n+1}< an+ L+ \epsilon$ so $a_n- k(L+ \epsilon)< a_{n+k}< a_n+ k(L+ \epsilon)$ is certainly true for k= 1. Now suppose $a_n- k(L+ \epsilon)< a_n< a_{n+1}+ k(L+ \epsilon)$ is true for some specific k and all n. Then $a_n- (k+1)(L+ \epsilon)= [a_n- (L+ \epsilon)]- k(L+\epsilon)< a_{n+1}-k(L+\epsilon)$ and now use $a_n- k(L+ \epsilon)< a_{n+1}$ with n+1 instead of n- which you can do because it is true for all n.

but i cant see in it my base (k) expression and using it to prove the (k+1) expression
i dont know how to apply it the step i got stuck
??

Last edited by a moderator: May 3, 2017
2. Jan 6, 2009

### transgalactic

http://img360.imageshack.us/img360/7791/63228047ot8.gif [Broken]

Last edited by a moderator: May 3, 2017