IIT JEE , AIEEE Forum - Mathematics , Algebra

chimanshu_007

important pts.

1) If T_p = P , T_q = Q in a GP then , T_n= { P^{n - q} / Q^{n - p}}^{1 / p - q}

2) T_{m + n}= P , T_{m - n} = Q in a GP then T_m =

PQ , T_n = p (q/p)^m/2n

3) T_m= n T_n = m in a HP then T_{m + n} = mn / m + n

4) T_p = qr T_q = pr in a HP then t_r = pq

chimanshu_007

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)

chimanshu_007

--->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}

vish0001

superb yaar !!! gr8 !!!!!

Arjun

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!!!!!!!!

chimanshu_007

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

KAB

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.

chimanshu_007

great one
cool

its_my_life_001

good......

chimanshu_007

thanx fr the rates :))

bhuvana89

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

thanx.....

keep it up.......

shinu.sharma

thanx u r the best yaarrrrrrrrrrrrrr

mrids_11

awesum yaar

chimanshu_007

Thanq :)

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