Limit of Sum as Integral
Should not both S and T be less greater than the required integral, i.e., pi/3sqrt(3)?
28 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.I am very confused. Tn = Sn - 1/3n for all n, and that means Tn is always less than the corresponding Sn.
I couldn't find a reliable way to compare Sn and S(n+1) though, so I have no way of saying whether {Sn} is a decreasing or increasing series
S_n must be increasing because positive terms are being added, right? And S_n must also be less than the integral required so wouldn't it be A and C?
Positive terms being added yes, but each term in S(n+1) is not the same as the corresponding term in Sn
Oh right, mb. Then we could look at it as a left reimann sum?
sometimes the website is wrong tho, what does the solution say?
That's the thing, it converges as n tends to infinity, but we don't even know if it's an increasing or decreasing series.
So we can't say anything about the values of Sn
It approaches the integral from below, so must be increasing right?
Yea, but janta is with the correct marked options with this one. :sweaty:
sometimes the answer is the 30% one while the 48% is wrong
doesn't necessarily have to be the majority
happened to me plenty of times
Ah. Will check once tommorrow.
alr
Official JEE Adv answer key says AD
Yeah it does. :/
I also looked at a few solutions and they seem to be converging on the following two points:
1. 1/(1+x+x^2) is decreasing in (0,1)
2. One claimed that Tn is the right riemann sum left riemann sum (which approaches from above, idk why I thought f is increasing) of the integral.
I fail to see how 1 is relevant and as for the other, for right riemann sum, shouldn't the range be 1 to n+1 and not 0 to n-1?
Oh wait I'm dumb, 1 and 2 are meant to be the same point ;;
But, then shouldn't the answer be B and D?
@Dexter
why am I summoned
Tumhara favourite topic
wait
one tends to n and one tends to n-1
that's making the difference innit?
Sochne wali baat hai
How is this conclusion drawn? 😭
@Jeeru Soda Sorry for the ping, but can you resolve this doubt? 🙏
Thoughts?
Sir where does the last statement come from?
Ah I see. One approaches from above the other from below?
I am forgetting the name of this property but as far as I remember I saw this in some coaching module
Old Allen or FIITJEE
Maybe taken from Maron's textbook
Ig the above question is misprinted over a lotta places :/
+solved @Jeeru Soda @Opt @Dexter @BlindSniper (BS)
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