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![[Post New]](/templates/default/images/icon_minipost_new.gif) 26 Mar 2007 20:50:31 IST
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Plz help me ith this question If S1,S2,S3............Sn denote the sum to 1,2,3,.......n terms of an AP having first term a and Skx/Sx is independent of x, then S1+S2+S3+.......Sn= ?
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-Ramya |
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26 Mar 2007 21:24:30 IST
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 Bcoz S(kx)/S(x)=does not depend on x therefore 2a+kxd-d/2a+xd-d=c where c is some constant.2a+kxd-d=2ac+cxd-cd 2a(1-c)+xd(k-c)-d(1-c)=0 2a(1-c),d(1-c) r constants so xd(k-c) must also b a constant. since x is chosen arbitrarily so either k=c(which is not necessary) or d=0. when d=0 then S(1)+S(2)+........+S(n)=na M i correct???
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26 Mar 2007 21:43:27 IST
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i got the method, but the answer is n(n+1)(2n+1)a/6
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-Ramya |
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Sorry I made some mistakes there. There r 2 possibilities CASE 1:When d=0 then S(n)=an soS(1)+S(2)+???+S(n)=an(n+1)/2 CASE 2:when k=c 2a-d=2ak-kd 2a(k-1)-d(k-1)=0 Either k=1(not necessary) or 2a=d S(n)=an^2 Then S(1)+S(2)+?..S(n)=an(n+1)(2n+1)/6 I hope this time I m correct.
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27 Mar 2007 01:01:05 IST
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yes absolutely. thanks a lot.
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-Ramya |
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