Question

2n C 0 + 2n C 1 + 2n C 2 +....................2n C n = 2^(2n-1)..is it true.
if yes or no, how??

Answer 1

What is C? Some constant? It's missing from the RHS..

Answer 2

combination sign..

Answer 3

n choose k?

Answer 4

n C r = {n!/(n-r)!r!}

now, can u understand my question?

Answer 5

yes, it's n choose k

Answer 6

i am not getting you...

Answer 7

It's the same thing, n choose k is a combination e.g. binomial coefficient

Answer 8

it's just another way of saying it :)

Answer 9

okay..

Answer 10

No.

Answer 11

It is false. It should be 2^n I think.

Answer 12

Take n=1 then 4 c 0 + 4 c 1 = 1 + 4 = 5 but 2^(2-1) is not 5.

Answer 13

No it should not be 2^n

Answer 14

You are correct it is not 2^n. I was thinking sum k=0 to n of n c k but that expression is sum k=0 to n of 2n c k

Answer 15

2^(2n-1).

Answer 16

I was speculating what the correct formula was...I said 2^n since sum k=0 to n of n c k = 2^n is a common identity but I forgot your expression was 2n c k.

Answer 17

Just ignore that post :) The identity is false. Just take n=1 for a counter example.