Total Price:

There are no items in this cart.
Continue Shopping

Sn = 1/1+√n + 1/2+√2n +.......+1/n+√n2

find limit n→∞ Sn

4 years ago


Answers : (1)


Dear Student

the sum can be written as ∑r=1r=n  1/(r + √rn)

= ∑r=1r=n  1/n(r/n + √r/n)

now replace 1/n by dx and r/n by x

limit of integral will be r/n

lower limit n tend to ∞ and r=1 will be 0

upper limit for r=n will be 1

it will convert into integral ∫01 dx/(x+√x) = ∫01dx/√x(1+√x)

now (1+√x)=t

and dx/2√x = dt

lower limit for x=0 , t=1 andupper limit for x=1, t=2

integral become ∫12 2dt/t= 2(lnt)12= 2ln2=ln4 answer


All the best.                                                           




Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation.

Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar  respectively : Click here to download the toolbar..





4 years ago

Post Your Answer

More Questions On IIT JEE Entrance Exam

Ask Experts

Have any Question? Ask Experts
Post Question
Answer ‘n’ Earn
Attractive Gift
To Win!!!
Click Here for details
SIr actually i am getting 113 marks in jee main should i start preparing for jee advance
Dear Student, Your marks are very close to previous year’s cutoff marks and this year predicted cutoff. Now given that paper was little tough this time, cutoff this year will go down...
Nishant Vora 11 days ago
your score is deadline on cutoff marks last year cut off was 115 lets hope for best prepare for bitsat and adv also approve if useful
ng29 11 days ago
i have take no coaching and i start just 10 day before jee main exam and expecting around 110 marks and 80% in cbse should i drop or can i get goood collage
if u are general category then your score is not enough for qualifying for jee main but you must prepare for other exams like bitsat and vitee in my opinion drop is very big decision and...
ng29 12 days ago
focus on ipu and viteeee approve if useful approve if useful approve if useful approve if useful
ng29 12 days ago
then can i get i desent college of this marks or am starting to focussing on ipu and viteee
rahak 12 days ago
How much in an hour would 40 cents a minute be?
Hmm... 40*60/(1/unit of cash in cents): -24 Dollars -48 Half Dollars -96 Quarters -240 Dimes -480 Nickels -2400 Cents -371.67 Pesos -$2.40 an hour -My Net worth -The budget for Plan 9 From...
TEJKIRAT SINGH one month ago
Hmm... 40*60/(1/unit of cash in cents): -24 Dollars -48 Half Dollars -96 Quarters -240 Dimes -480 Nickels -2400 Cents -371.67 Pesos -$2.40 an hour -My Net worth -The budget for Plan 9 From...
vikas yadav one month ago
How The Global Positioning System works?
The Global Positioning System (GPS) is a satellite based navigation system developed by the United States Department of Defense. It is widely used for civilian navigation and positioning,...
Radhika Batra 6 years ago
i want to crack AIPMT how to prepare and what type of books are useful for me
Understand the Syllabus throughly, specially which individual sections are important.Prepare beginning from Class 11 syllabus before moving on to Class 12. Make sure you are clear on the...
Dinesh 10 months ago
Hi! I didnot receive the VITEEE 2015 online slot booking password till now. Can u pls guide me what should I do to get the password. Kindly provide me the procedrure if any
Hi Student, Dont get panic. Please visit the official website of VITEE. You have the contact details for custumer service. Please inform the same and retrieve the password
Harishwar 28 days ago
Hi student, Please go their website and try to contact the people who conduct the test thanks,
Nishant Vora 28 days ago
View all Questions »