17 Replies
@Apu
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.
Also if you don't mind, what is the source of the question?
This is a pretty good question
Ye exactly.
Our sir gave the ques by their
maybe its a original ques created by him
or taken from some book
Ah I see.
Please explain the first step
how f(x) < x
fr but I am right now dumb for it
I subtly imporiving it will take time
f(x+1) - f(x) ≤ (x+1) - (x) for all x.
oh
how do you get to know how to transform it
like intead of writing 1
Practice.
you did
I do still
thinkinh of approach takes too much time
It does yeah
:sweaty:
Oh sorry mb.
Consider the following inequalities:
f(x+1)-f(x)<=1
f(x)-f(x-1)<=1
and so forth till f(2)-f(1)<=1
Add all these and you get f(x+1)<=x+f(1)=x+1
So f(x+1)<x+1 or f(x)<x
Or just look at it like this: difference between f(x+1) and f(x) will be at max 1. So the max. value of f(x) can be attained for x in natural when f(1),f(2)... are terms of an A.P. with common difference 1.
yo ugood?