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Algebra

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30 Mar 2007 20:10:54 IST

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4968

AP GP HP is nt difficult

None

important pts. 1) If Tp = P , Tq = Q in a GP then , Tn = { 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

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Comments (16)

Himanshu

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Joined: 19 Feb 2007

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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

a^{n + 1}+ b^{n + 1} / aⁿ + bⁿ = A when n=0

a^{n + 1}+ b^{n + 1} / aⁿ + bⁿ= B when n = -1/2

a^{n + 1}+ b^{n + 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

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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
T_p+q = 0
T_r = p + q - r

---> pT_p = qTq of an AP then

T_{P+q = 0}

vishak p

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30 Mar 2007 23:15:57 IST

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superb yaar !!! gr8 !!!!!

Arjun

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30 Mar 2007 23:36:08 IST

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some more..........

if for a G.P, T_p=p,T_Q=q, T_n=[p^n-Q/q^n-p]^1/p-q

If for a G.P T_m+n=p, T_m-n=q thenT_m=sqr rt(pq), T_n=p(q/p)^m/2n

==>if a,b,c, are the pth,qth,rth terms of a G.P then a^q-r.b^r-p.c^p-q=1

==> aⁿ⁺¹+bⁿ⁺¹/aⁿ+bⁿis G.M betwen a and b if n=1/2

thank u!!!!!!!!

Himanshu

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31 Mar 2007 12:09:54 IST

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good one arjun!!!!!!!!!!!!!

CyBorG

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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+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

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31 Mar 2007 22:04:10 IST

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great one
cool

rahul singh

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Joined: 12 Apr 2007

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23 Apr 2007 15:25:03 IST

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good......

Himanshu

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19 May 2007 19:32:44 IST

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thanx fr the rates :))

bhuvana........

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25 Aug 2007 00:49:50 IST

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awesome................xtremely .useful.........

thanx.....

keep it up.......

shinu sharma

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Joined: 3 Apr 2007

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2 Sep 2007 14:27:48 IST

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thanx u r the best yaarrrrrrrrrrrrrr

mridu ....

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Joined: 8 Jan 2008

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27 Jan 2008 20:59:52 IST

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awesum yaar

Himanshu

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Joined: 19 Feb 2007

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27 Jan 2008 22:15:09 IST

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Thanq :)

svj 29

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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..

.......Eshita.......!!!!

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15 Feb 2009 22:00:56 IST

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hey,svj..ur trick wz awesum..

thnx..

Chitra Pandey

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Joined: 15 Apr 2008

Posts: 96

28 Mar 2009 22:10:58 IST

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thnk ya..

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