What is V n method?? plzz replyy its urgent

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JOEL JOHNSON · Answer

to find the sum of the following form, 1/a 1 a 2 a 3 .....a r + 1/a 2 a 3 .....a r+1 +..........1/a n a n+1 .....a n+r-1 where a 1 , a 2, ............, a n,....... are in A.P we use the v n method. sol: let d be the common difference let the sum of the series and nth term be denoted by S n and T n S n =1/a 1 a 2 ......a r +................+ 1/a n a n+1 .....a n+r-1 T n = 1/a n a n+1 ......a n+r-2 a n+r-1 let V n = 1/a n+1 a n+2 ........a n+r-1 so, V n-1 =1/a n a n+1 ...........a n+r-2 V n -V n-1 = a n -a n+r-1 /a n a n+1 ....a n+r-2 a n+r-1 V n -V n-1 = T n (a n -a n+r-1 ) after expanding and simplifying we get V n -V n-1 =d(1-r)T n T n =(v n -V n-1 )1/d(r-1) putting n=1,2,3,.....,n T 1 =(V 0 -V 1 )1/d(r-1) T 2 =(V 1 -V 2 )1/d(r-1) …...................................... …...................................... T n =(V n -V n-1 )1/d(r-1) adding the above equations, T 1 +T 2 +...........+T n =(V 0 – V n )1/d(r-1) substitute the values of V 0 and V n in the equation. this is the V n 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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What is V n method?? plzz replyy its urgent

What is Vn method?? plzz replyy its urgent

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