IIT JEE , AIEEE Forum - Mathematics , Algebra - anybody has a god question in mathematics ???

rebel

heyyyy.. that 's a cool, short but superb question ! ya... u can do it with signum one now... gud thanks... take a rate for this !

harshiiit

now how do v integrate sgn xpower n

Avinash_Bhat

Hey rebel, it's not (a) for ' tricky no.1 ' now please don't go on confirming each option yaar....!! This is really a tricky question and.. you want the answer.... or you want to continue your effort to kill the question...?? You can do it, come on...

Oh... before this, someone pleazzzz answer this :

Simplify : (1 + sin

+ icos

)ⁿ / (1 + sin

- cos

)ⁿ

A little starting trouble over here...

rebel

sorry bro......... i think that i can do this quest..... but no more is coming to my mind this moment.... as there is shortage of time..... can u please tell me the answer ???

sorry yaar......

rebel

and for tje above question..... it's easy man..... write 1 = iota to the power 4 !

Avinash_Bhat

Thanx for that....and let me now kill that tricky question :

As per the qn, there are 6t terms in an A.P. S1 : sum of first 2t terms

S2 : sum of first 4t terms

S3 : sum of last 2t terms

I believe, you know this : given 3n terms of an A.P.,

Sum of 1st n terms, Sum of next n terms, Sum of last n terms are in A.P.

Then here S1, (S2 - S1), S3 are in A.P. ---------- (1)

Also given, (S1*S2*S3 - S1^2*S3) = 4;

ie, S1*(S2 - S1)*S3 = 4

A.M. >= G.M.

{ S1 + (S2 - S1) + S3 } / 3 >= cuberoot(S1*(S2 - S1)*S3)

>= cuberoot(4)

From eqn(1) 3(S2 - S1) / 3 >= cuberoot(2^2)

(S2 - S1) >= 2^2/3

SO : (S2 - S1) not less than 2^2/3 .........

You like it???

"Thathwamasi"

Avinash_Bhat

Someone answer pleazzz:

(1 + x)n = a₀ + a₁x + a₂x² + .... + a_nxⁿ, then prove that :

( i ) a₀ - a₂ + a₄ - a₆ + ........ = 2^n/2 cos(npie / 4)

( ii ) a₁- a₃+ a₅ - a₇ + ......... = 2^n/2 sin(npie / 4)

I' m getting many blocks on my way to this one...Explain ok??

rebel

areyyyy yaar !!! really speaking i was so close......................................................... shit man..... i wanna kick myself..........................hey this was not at all tricky....... i mean that's a different story that i couldn't solve.aneways thankx !!!!!
take a rate !

Avinash_Bhat

Thanx rebel.
Now.......
Someone pleazzzzzzzzz answer my last question

And someone...pleazzz send good questions on " progressions ", including A.P., G.P., H.P., special series etc..

rebel

yaar.do it by substotuing x =1..in the expression in lhs of (1+x)^n
then...separate the even and odd terms.....
u will get it....

Avinash_Bhat

Thanx yaar..

KAB

(i)First put x=i and then put x= -i and add them.
Then apply De'Moivres theorem for simplification of (1+i)^n+(1-i)^n
(ii)Here you have to subtract and you will get the answer.

rebel

any other one ??

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