Mera bhi ek binomial (its easy)

Prove that-
2C01+22C12+23C23+...+2n+1Cnn+1=3n+1-1n+1

13 Answers

24
eureka123 ·

ya really very easy

(1+x)^n=C_0+c_1x+C_2x^2+....
inegrating wrt x, limits 0 to 2

\int_{0}^{2}(1+x)^n=\int_{0}^{2}[C_0+c_1x+C_2x^2+....]

u will get teh ans

1
Philip Calvert ·

@eureka.

what about the binomial coefficients.
in your expression they are nCr
but in the question something totally different.

maybe something in hidden layers i cannot see. so just elaborate a bit in that case ?.

24
eureka123 ·

@ philip....
how can index of expansion change ????

teh coeff in ques are 2.C01+ 22.C12+..
and not 2C01+ 22C12+..
[1]

1
Unicorn--- Extinct!! ·

No dude, its its the latter case!!
I think I had it written clearly.[7]

24
eureka123 ·

It cant be the latter case.....how can the index change ????

21
eragon24 _Retired ·

eureka is right[1]

24
eureka123 ·

though i will be glad if u porve me wrong.. and show up ur soln

1
Unicorn--- Extinct!! ·

But that is the question...
(or there must be a misprint??)

1
Unicorn--- Extinct!! ·

I can't prove you wrong. I found fault in my solution[2][4]

24
eureka123 ·

surely misprint.....

but u said u have proved it..tell me how u did taht [6]

1
Unicorn--- Extinct!! ·

Bhai eureka, I said that I found fault in my solution...u want the wrong proof?? I can give you that...
But not here(Apni public insult nahi karani!!!)[14]

24
eureka123 ·

kkkkkkkkk

no prob dude.....maybe ididnt get ur point....
anyways ur prob solved now.thats the best thing[1]

1
prongs05 ·

2, 22, 23, ..... etc. are not the index (n)..but they r the co-efficients of C0, C1,, C2,..etc....

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