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What is V n method?? plzz replyy its urgent

What is  Vn method?? plzz replyy its urgent

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1 Answers

JOEL JOHNSON
35 Points
7 years ago
to find the sum of the following form,
1/a1a2a3.....ar    +  1/a2a3.....ar+1    +..........1/anan+1.....an+r-1
where a1, a2, ............, an,....... are in A.P
we use the vn method.
 
sol: let d be the common difference
     let the sum of the series and nth term be denoted by Sn and Tn
Sn=1/a1a2......ar  +................+ 1/anan+1.....an+r-1
Tn= 1/anan+1......an+r-2an+r-1
let Vn= 1/an+1an+2........an+r-1
so, Vn-1=1/anan+1...........an+r-2
 Vn-Vn-1= an-an+r-1/anan+1....an+r-2an+r-1
 Vn-Vn-1= Tn(an-an+r-1)
after expanding and simplifying we get
Vn-Vn-1=d(1-r)Tn
Tn=(vn-Vn-1)1/d(r-1)
putting n=1,2,3,.....,n
T1=(V0-V1)1/d(r-1)
T2=(V1-V2)1/d(r-1)
…......................................
…......................................
Tn=(Vn-Vn-1)1/d(r-1)
adding the above equations, 
T1+T2+...........+Tn=(V0 – Vn )1/d(r-1)
substitute the values of V0 and Vn in the equation.
this is the Vn method however this formula should not be used directly in subjective questions.
took half hour to type in all symbols and subscripts cheers mate!!!!!!!

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