MY CART (5)
ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price:

There are no items in this cart.
Continue Shopping
                   

Sum  to  n    terms      


 


3.7.11.15+7.11.15.19+................... 


 


Dont post the full solution,Maybe Hints(Like the method )


 


Should we use factorial things in here???


 


 

3 years ago

Share

Answers : (14)

                                        

The biggest hint to theis problem tht the question can be done using Vn method. Search it. Try it

3 years ago
                                        

Do u know the Vn method ??

3 years ago
                                        

At Swapnil Saxena : Thanks for the hint.How do u know these kinda of methods?




V-n method




V-n method is used to solve the series summation problem in the fom of :


 


1> 1/(a1*a2)  +  1/(a2*a3)  +  1/(a3*a4)  +........ upto n terms


 


2>(a1*a2)  + (a2*a3)  +  (a3*a4)  +.............upto n terms


 


where a1,a2,a3 ..... are in AP with certain common difference


 

3 years ago
                                        

hi swapnil


this question cannot be done by VN method!!!!


see and guess why this question is not done by VN method

3 years ago
                                        

@ Samarth : No Idea??? Why... Tell me. Is there is something wrong. This is wht u told me.


@ Sathyaram : Good Friendship, attempts, courage, and hard labour always pays...


@ Jit: Sathyaram is right... but I wanna further extend . Not just the series like tht but like


a1a2a3a4a5+ a2a3a4a5a6 +a3a4a5a6a7 .... or 1/a1a2a3a4a5+ 1/a2a3a4a5a6 + 1/a3a4a5a6a7 ....  like difficulties can be solved by this method  

3 years ago
                                        

Hi Guys,


 


This question can definitely be solved using the Vn method.


S = Σ(4r-1)(4r+3)(4r+7)(4r+11), r=1,2,3,....n.


So Tr = (4r-1)(4r+3)(4r+7)(4r+11)


and let Vr = (4r-5)(4r-1)(4r+3)(4r+7)(4r+11)


hence, Vr+1 = (4r-1)(4r+3)(4r+7)(4r+11)(4r+15)


 


So Vr+1 - Vr = 20xTr.


Hence Σ(Vr+1 - Vr) = 20*S


Hence S = (1/20)*[Vn+1 - V1] = (1/20)*[(4n-1)(4n+3)(4n+7)(4n+11)(4n+15) + 3.7.11.15] ------- (Required Answer).


 


Regards,


Ashwin (IIT MadraS).

3 years ago
                                        

Agree with swapnil. Lemme try to generalize it for u.


 


S = a1a2a3a4a5....ar + ar+1ar+2ar+3ar+4....a2r +    ..............  + an-r+1an-r+2an-r+3......an


 


Tn = an-r+1an-r+2an-r+3......an


 


Vn = anan+1an+2......an+r-1an+r


(Take an extra Last Term in Vn)


 


Vn-1 = an-1anan+1......an+r-2an+r-1


 


Vn - Vn-1 = anan+1an+2......an+r-1 [an+r - an-1 ] = Tn[an+r - an-1 ] = Tn [{a1 + (n+r-1)d} - {a1+ (n-2)d}] = Tn [(r+1)d]


 


or, Tn = 1/[(r+1)d] * [Vn - Vn-1]


 


Now put n=1,2,3,....,n and add.


 


T= 1/[(r+1)d] * [V1 - V0]


T= 1/[(r+1)d] * [V2 - V1]


T= 1/[(r+1)d] * [V3 - V2]


.


.


.


.


T= 1/[(r+1)d] * [Vn - Vn-1]


______________________________


S = 1/[(r+1)d] * [Vn - V0]


 


From here you can find the sum easily.


 


Similarly for the sum of reciprocals, Take one term less for Vn .

3 years ago
                                        

@ Ashwin Sir,


Thanks for ur answer and ur answer is correct...


 


But, How could u assume that "let Vr = (4r-5)(4r-1)(4r+3)(4r+7)(4r+11)"?


 


And where did (4r-5) go in this equation? :


Vr+1 = (4r-1)(4r+3)(4r+7)(4r+11)(4r+15)

3 years ago
                                        

Dude,


 


Enna idhu Sir lam... :P


Seri adhe vidu.


 


Vr is assumed based on the Tr.


In Vr we assume one more term in the start.


 


If Vr = (4r-5)(4r-1)(4r+3)(4r+7)(4r+11)


then replace r by r+1 in this to get Vr+1.


Hence you get Vr+1.


 


Regards,


Ashwin (IIT Madras).

3 years ago
                                        

Pingilikka pillaaapi ,Summa said.


 


Can u do this without Vn method ?I am kinda new to this and not feelin comfortable...

3 years ago
                                        

Dude,


 


Then please get comfortable with it.


It is really easy.


 


Regards,


Ashwin (IIT Madras),

3 years ago
                                        

Periya manishan,Neenga solitengala.......Ill get comfortable  :)  Laughing  


 


And also,I have send u sme mails in gmail......Pls look at it

3 years ago
                                        

Dude,


 


Done!!


Hope that you take those mail replies seriously. Now you prepare and do your Boards well.


 


You can think about your 11th Std after your exams :).


Wish you all the best.


 


Regards,


Ashwin (IIT Madras).

3 years ago
                                        

Oh k.Thnks.I have sent u  reply....Pls look at it and dont forget to c mokkais ! Tongue out


And in Biology CBSE,


I dont understsnd these mendels cross breeding,dominant,recessice...Could u just help me out... :)

3 years ago

Post Your Answer

More Questions On Algebra

Ask Experts

Have any Question? Ask Experts
Post Question
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details
if a>0 and x>y the show that a^x+a^-x>a^y+a^-x
 
 
Both the sides contain a common exponenta^x+ a^-x >a^y+ a^-x Eliminate the exponent first. As x>y, and a>0 so a^x>ay...
  img
Ravi 3 months ago
x-y=2+2y
 
 
I don’t know exactly what do you need but x-y=2+2y x-2=3y x-3y=2 this is what you can do you can’t do it futher
 
Jonathan Jackson 2 months ago
 
I don’t know exactly what do you need but x-y=2+2y x-2=3y x-3y=2 this is what you can do you can’t do it futher
 
Jonathan Jackson 2 months ago
hey image attached please tell the method which is used in solution …..please sir .maam …..please anyone …...
 
 
Ans: Hello student, Please find the answer to your question below [] is greatest integer function. Now looking at the problem in hand There are total 100 term in L out of which 25 terms are...
  img
Jitender Singh 5 months ago
What is the value of ∫ e -x (1-tanx)secx dx .
 
 
Hi, Just differentiate your answer with respect to x, if you are getting the original function (as in the question), then your answer is correct, otherwise wrong....
  img
Shobhit Varshney 4 months ago
 
Hi, Please use the integration formula by parts and take e-x to be first function and the remaining to be second...
  img
Shobhit Varshney 4 months ago
 
I just want the answer to see whether my answer is correct or not.
 
Shibashis Mallik 4 months ago
PLZ HELP STUCK WITH THIS FOR HOURS!! A regular hexagon ABCDEF with centre O,show that: __ __ __ __ 1.OB - OA = OC - OD __ __ __ __ 2.OD + OA = 2OB + OF __ __ __ __ 3.AD + EB + FC = 4AB
 
 
Something missing in the question. Concepts that are useful here length of points from center all equal. Triangle formed by center and 2 consecutive points is equilateral. Arun Kumar IIT...
  img
Arun Kumar 9 months ago
View all Questions »