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Sathya Grade: 10
        

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???


 


 

5 years ago

Answers : (14)

Swapnil Saxena
102 Points
										

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

5 years ago
Jit Mitra
25 Points
										

Do u know the Vn method ??

5 years ago
Sathya
35 Points
										

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


 

5 years ago
samarth saxena
37 Points
										

hi swapnil


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


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

5 years ago
Swapnil Saxena
102 Points
										

@ 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  

5 years ago
Ashwin Muralidharan IIT Madras
290 Points
										

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).

5 years ago
Jit Mitra
25 Points
										

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 .

5 years ago
Sathya
35 Points
										

@ 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)

5 years ago
Ashwin Muralidharan IIT Madras
290 Points
										

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).

5 years ago
Sathya
35 Points
										

Pingilikka pillaaapi ,Summa said.


 


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

5 years ago
Ashwin Muralidharan IIT Madras
290 Points
										

Dude,


 


Then please get comfortable with it.


It is really easy.


 


Regards,


Ashwin (IIT Madras),

5 years ago
Sathya
35 Points
										

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


 


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

5 years ago
Ashwin Muralidharan IIT Madras
290 Points
										

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).

5 years ago
Sathya
35 Points
										

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... :)

5 years ago
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