Sequence. (1 Viewer)

[Fus Ro Dah]

 

[RealiseNothing]

I got 0 lols.

Not sure what happened there.

 

[Fus Ro Dah]

Sorry, I made a typo. The first term should read T_{n+1}.

 

[RealiseNothing]

Sorry, I made a typo. The first term should read T_{n+1}.

Ah k, I was wondering why everything cancelled out.

 

[barbernator]

don't we need the value of T0 or something to evaluate T2012?

 

[bleakarcher]

Don't we need some initial condition in order to find T_2012 like the value of T_0?

 

[barbernator]

don't we need the value of T0 or something to evaluate T2012?

Don't we need some initial condition in order to find T_2012 like the value of T_0?

lol

 

[Fus Ro Dah]

My apologies, everybody. I am not thinking clearly at the moment. The initial value T_0 = T.

 

[bleakarcher]

lol

lol, it's happened quite a bit to me lately.

 

[barbernator]

<a href="http://www.codecogs.com/eqnedit.php?latex=\frac{T}{1@plus;4044121T}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\frac{T}{1+4044121T}" title="\frac{T}{1+4044121T}" /></a> edited.

?

 

[Fus Ro Dah]

Please explain how you acquired that answer.

 

[RealiseNothing]

The sequence becomes:



Wait maybe not, re-checking working.

 

[RealiseNothing]

On second attempt, and this time not adding an extra 'T' which screwed me up before I get:



Where denotes the k'th triangular number.

 

[seanieg89]

Falls apart from the substitution S_n=1/T_n.

In the case T=1 this yields: T_n= 2/(n^2-n+2).

 

[RealiseNothing]

Since triangular numbers can be worked out using we get:



Therefore:

 

[barbernator]

Please explain how you acquired that answer.

subbed in twice and observed pattern... lol. Is it correct?

 

[deswa1]

subbed in twice and observed pattern... lol. Is it correct?

Haha I do this for so many questions. Not sure if you're right- haven't looked at the question. I think this question is the only one out of the set of like 4 that Fus just posted that I'll have a chance at solving lol

 

[Sy123]

??

 

[RealiseNothing]

??

I'm pretty sure your 5th line should be:

 

[Sy123]

I'm pretty sure your 5th line should be:

Ah yes of course, oops :/
Then yeah it would work out to your answer