MY CART (5)
ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
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

Share

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.                                                           


AKASH GOYAL


AskiitiansExpert-IITD


 


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
Vouchers
To Win!!!
Click Here for details
Can i download JEE Main and Advance IIT materials
 
 
Hii Please find the link to download study material for IIT :- http://www.askiitians.com/iit-study-material/...
  img
Amit Shekhar 5 months ago
If r,s,t are prime numbers and p,q are the positive integers such that L.c.m of p,q is r 2 s 4 t 2 ., then the total number of ordered pairs(p,q) is ??
 
 
sorry it is incorrect solution, i mistakened it for factors rather than lcm question Correct solution Selection for p &q p q ways r 0 r 2 1 r 1 r 2 1 r 2 r 0 , r 1, r 2 1 Total way to select...
 
Abhishek Singh one month ago
 
no. of pais possible=3*5*3=45
 
Abhishek Singh one month ago
What is the final product when ethyne reacts with HCN? Is hydrogenation of alkenes and alkynes a syn addition?
 
 
1 CHCH +HCN ----------CH2CH(CN) 2)Yes hydrogenation of alkene is a syn addition.The unsaturated substrate is chemisorbed onto the catalyst, with most sites covered by the substrate. In...
  img
Sunil Kumar FP 3 months ago
 
  img
Sunil Kumar FP 3 months ago
 
Please explain in detail how adsorption is related to syn and anti orientations in reactions.
 
Himaja 3 months ago
A disk like reel with a mass-less thread unrolls while falling vertically downwards. The acceleration of its free fall is?? If there is no mass in the thread how will acceleration take...
 
 
If mass of disc(cylinder like reel) is considered only. then Torque equation, calculate torque due to tension about the centre, T X R = I x angular acceleration Force equation, mg – T...
  img
Saurabh Kumar 4 days ago
If one gets 189 in jee mains and has 94% in cbse boards, will he get mnit allahabad ec or dtu ec.
 
 
If one gets 189 in jee mains and has 94% in cbse boards, getting mnit allahabad ec or dtu has very low chances as these branches close at much better ranks.
  img
Sher Mohammad 7 months ago
View all Questions »