Time Complexity of iterative series

Question

What should be the time complexity of :

k=1;
while (k<=n) do      
    j=1;
    while (j<=k) do        
        sum=sum+1;
        j=j+1;
    k=k*2;

According to me:
For K=1, j= 1 time

for K=2, j=2 times

For K=4, j=4 times..

And so on...

Thus sum= 1+2+4+8....n

This is I think 2n+1-1

So should the answer be O(2n) ?

Comments

Thus sum = 1 + 2 + 4 + 8 + ..... log(n)   /// while(k<n)

So, T(n) = (2^log(n)+1 - 1) / (2-1)

               = O(n).

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1+2+2^2+2^3+2^4+.+2^k is in geometric progression

solving it we get 2n-1 i.e O(n)

Answer 1

Let Consider $n = 2^k$

Then total work done by the inner loop is 

$T(n)$ = $2^0$ + $2^1$ + $2^2$ + $2^3$ + $2^4$ + ..................... + $2^k$

        <= $2^{(k+1)}$

        <= $2^{((logn)+1)}$

        <= $2n$

$T(n) = O(n)$. This will be the correct time complexity of the above code snippet.