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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

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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

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