@Aasthachoudhary you can come here

Hi!

Please elaborate that portion.

Yeah

So I am not really fast at mathjax and as I too am preparing for entrances, I do not have too much time to type it, yet I will try; please follow with pen-paper or something:)

That's completely fine.

First of all it is helpful to notice that 1/2+1/3=5/6. 5/6+1/7=41/42. In entrance environment that will lead you to answer already

yes, that way I also observed.

Secondly, for my formula, it was clear till 1+1/a_n right?

that one term

yes upto that only!

now $a_{n}-1$ would give plainly the fraction $\frac{1}{a_{n-1}+\frac{1}{a_{n-1}-1}}$

and this is the denominator

yes

there would be a fraction upon a fraction. which can be moved up

sorry?

This is kinda continued fraction but not actually continued. Isn't?

to give something like $a_{n}+a_{n-1} $ in denominator

yeah

it is

continued

okay!

simple typing is fine

mathjax is time consuming.

see in the fraction I have shown a_(n-1) in denominator. Applying the same formula as that to a_n - 1 gives a fraction upon a fraction

yes basically like continued fraction.

yeah so it leads to $a_{n+1}=1+\frac{1}{a_n+a_{n-1}...a_1+\frac{1}{a_1-1}}$

yes..

so adding this to sigma a_n gives the required formula after some manipulations

I did not try anything further, though that formula seems helpful

okay! So this was the usage of the given condition again and again!

yeah! Thanks for your efforts btw what exams are you preparing for?

yeah. I do not know whether you were taught number theory in college, but I don't think students are taught except in iisc or isi

I am preparing for IISc undergrad entrance KVPY

or maybe CMI or ISI

Sadly, I am not shortlisted for ISI :(

And JEE Advanced

@AasthaChoudhary woops

CMI is better

No! they are not taught!

yeah, So this was the formula only

@DevanshBhardwaj undoubtedly its better.

@AasthaChoudhary Well try cmi then

Sure! Good luck!

CMI undergrads have went to PhD in Princeton (9 students) and princeton is best for math PhD

We get to attend IAS lectures

Wow IAS lectures!

@AasthaChoudhary Thanks. I am in last year so I have 1 year to prepare

That's great!

I am referring to Institute of Advanced Study, that would be clear:)

yeah!

I am not aware of advanced study

Thanks for giving your time; I wanted to talk about that for so along

@AasthaChoudhary what?

Institute of Advanced Study!

ias.edu

Thanks again :)

Welcome. I hope CMI does shortlist you:)

and again IISc is just as good for mathematics

Hopefully!

undoubtedly IISc is,let's see!

Im leaving this room undeleted, so if I happen to answer or comment again and you want to discuss, just ping me here

And are there not sources for MCQ solutions on internet? I think they are not really promoted on stackexchange.

@AasthaChoudhary You are welcome. Bye :)

Bye!

:)

Asking for sources on internet for mcqs?

yeah! not promoted on stack.