# Find value of C0+(C0+C1)+(C0+C1+C2)+(C0+C1+C2+C3).

1. Dec 9, 2011

### vkash

find value of C0+(C0+C1)+(C0+C1+C2)+(C0+C1+C2+C3).......

Cr represent nCr
find the value of C0+(C0+C1)+(C0+C1+C2)+(C0+C1+C2+C3).......(C0+C1+C2+C3+.....Cn)

How i did it
C0+C1+C2+.........Cn=(1+1)n
so
C0=(1+1)0
C0+C1=(1+1)1 ( here n is 1)
C0+C1+C2=(1+1)2 (here n is 2)
.
.
.

so the required question is changed into following
20+21+22+23+..........+2n
that's Geometric progression
so it should equal to 2n-1

where i have done it wrong

2. Dec 9, 2011

### eumyang

Re: find value of C0+(C0+C1)+(C0+C1+C2)+(C0+C1+C2+C3).......

Your notation is ambiguous. If Cr = nCr, then I would think that
C0 = nC0 = 1,
C0 + C1 = nC0 + nC1 = 1 + n,
C0 + C1 + C2 = nC0 + nC1 + nC2 = 1 + n + n(n+1)/2.

It looks like when you were finding
C0+(C0+C1)+(C0+C1+C2)+(C0+C1+C2+C3).......(C0+C1+C2+C3+.....Cn)
you were actually finding
0C0 + (1C0 + 1C0) + (2C0 + 2C0 + 2C0) + ... + (nC0 + nC0 + nC0 + ... + nC0).

So which one are you looking for, exactly?

3. Dec 9, 2011

### vkash

Re: find value of C0+(C0+C1)+(C0+C1+C2)+(C0+C1+C2+C3).......

my question was correct.
You did not answer the question but you answer you have solved my problem. that is always nCr. I take different values of n. that's what i was doing wrong.
Thanks Bcz you put out difference in my answer and question.
Thanks friend.

4. Dec 9, 2011

### Ray Vickson

Re: find value of C0+(C0+C1)+(C0+C1+C2)+(C0+C1+C2+C3).......

Assuming you mean C(k) = nCk for k = 0, 1, 2, ..., n, your sum, S, can be expressed as
$$\begin{array}{l}S = (n+1)C(0) + n C(1) + (n-1) C(2) + \cdots + C(n) \\ \mbox{ } = (n+1)[C(0) + C(1) + \cdots + C(n)] - [C(1) + 2C(2) + \cdots + nC(n)], \end{array}$$
and this last sum can be computed (do you see how?)

RGV