Sum of powers

Take the code sample below:

for (int i = 1; i <= N; i *= 2)
    for (int j = 1; j <= i; j++)
        x++;

As discussed earlier, the outer loop runs $(logN + 1)$ times. The number of times the inner loop runs is equal to the first loop variable $i$.

• Iteration $1$: Inner loop runs for $1$ time
• Iteration $2$: Inner loop runs for $2$ times
• Iteration $3$

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