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What is V n method?? plzz replyy its urgent What is Vn method?? plzz replyy its urgent
to find the sum of the following form,1/a1a2a3.....ar + 1/a2a3.....ar+1 +..........1/anan+1.....an+r-1where a1, a2, ............, an,....... are in A.Pwe 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 TnSn=1/a1a2......ar +................+ 1/anan+1.....an+r-1Tn= 1/anan+1......an+r-2an+r-1let Vn= 1/an+1an+2........an+r-1so, 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 getVn-Vn-1=d(1-r)TnTn=(vn-Vn-1)1/d(r-1)putting n=1,2,3,.....,nT1=(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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