Algebra

Himanshu's Avatar
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30 Mar 2007 20:10:54 IST
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AP GP HP is nt difficult
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

important pts.
 
1) If Tp = P , Tq = Q in a GP then , T= { Pn - q / Q n - p }1 / p - q
 
2)  Tm + n = P  , Tm - n = Q in a GP then Tm = PQ   ,  Tn = p  (q/p)m/2n
 
3) Tm = n        Tn = m in a HP then Tm + n = mn / m + n
 
4) Tp = qr        Tq = pr in a HP  then tr = pq



Comments (16)

Himanshu's Avatar

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30 Mar 2007 20:20:10 IST
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A , G , M  are the AM ,  GM ,  HM b/w a and b then
 
an + 1 + bn + 1 / an + bn = A when n=0
 
an + 1 + bn + 1 / an + bn = B when n = -1/2
 
an + 1 + bn + 1 / an + bn = C when n = -1
 
 
-------> If
a - b / b - c
 = 1 (abc are in AP)
 = a/b (abc are in GP)
 = a/c(abc are in HP)
Himanshu's Avatar

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30 Mar 2007 21:02:13 IST
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--->In an AP , if a is the 1st term , d is the common diff. , having m terms then nth term frm end is a + (m - n )d
--->Relation b/w AM GM HM
A > G > H and  AGH are in GP  G2 = AH
---> If pth term of an AP is q and qth term is p then
Tp+q = 0
Tr = p + q - r
---> pTp = qTq of an AP then
T P+q = 0
vishak p's Avatar

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30 Mar 2007 23:15:57 IST
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superb yaar !!! gr8 !!!!!
Arjun's Avatar

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30 Mar 2007 23:36:08 IST
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some more..........
 
if for a G.P, Tp=p,TQ=q,   Tn=[pn-Q/qn-p]1/p-q
 
If for a G.P Tm+n=p, Tm-n =q thenTm=sqr rt(pq), Tn=p(q/p)m/2n
 
==>if a,b,c, are the pth,qth,rth terms of a G.P then aq-r.br-p.cp-q=1
 
==> an+1+bn+1/an+bn is G.M betwen a and b if n=1/2
 
thank u!!!!!!!!
 
 
 
 
 
Himanshu's Avatar

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31 Mar 2007 12:09:54 IST
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good one arjun!!!!!!!!!!!!!
CyBorG's Avatar

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31 Mar 2007 13:21:43 IST
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Here are some more!
 If A and G be the AM and GM between two numbers a,b then a,b are given by
A (A+G)(A-G)
 
If H is the HM between a and b then,
(H-2a)(H-2b)=H2
(1/(H-a))+(1/(H-b))=(1/a)+(1/b)
((H+a)/(H-a))+((H+b)/(H-b))=2
 
If a,b,c are any numbers then,
a3+b3+c3-3abc=(a+b+c)(a+bw+cw2)(a+bw2+cw)
where w is cube root of unity.
Himanshu's Avatar

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31 Mar 2007 22:04:10 IST
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great one
cool
rahul singh's Avatar

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23 Apr 2007 15:25:03 IST
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good......

Himanshu's Avatar

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19 May 2007 19:32:44 IST
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thanx fr the rates :))
bhuvana........'s Avatar

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25 Aug 2007 00:49:50 IST
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awesome................xtremely .useful.........
 
thanx.....
 
keep it up.......
shinu sharma's Avatar

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2 Sep 2007 14:27:48 IST
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thanx u r the best yaarrrrrrrrrrrrrr
mridu ....'s Avatar

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27 Jan 2008 20:59:52 IST
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awesum yaar
Himanshu's Avatar

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27 Jan 2008 22:15:09 IST
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Thanq :)
svj 29's Avatar

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12 May 2008 02:20:18 IST
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one more for objective approach:

2,3,6 are three numbers in HP

3,4,6,12 are four numbers in HP

juz put the values n get the answer..

New kid on the Block

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15 Feb 2009 22:00:56 IST
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hey,svj..ur trick wz awesum..

thnx..

Chitra Pandey's Avatar

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28 Mar 2009 22:10:58 IST
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thnk ya..



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