Problem

4. Determine the following summation $\sum_{i=0}^{8}\left(\begin{array}{l}8 \\ i\end{array}\right)$ (2 marks)

Answer

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Answer

\(\boxed{256}\) is the summation of the binomial coefficients for n=8 and i ranging from 0 to 8

Steps

Step 1 ：Calculate the binomial coefficients for each i using the formula: \(C(n, k) = \frac{n!}{k!(n-k)!}\)

Step 2 ：Sum the binomial coefficients for n=8 and i ranging from 0 to 8: \(\sum_{i=0}^{8}\left(\begin{array}{l}8 \\ i\end{array}\right)\)

Step 3 ：Using Python, we find the summation to be 256

Step 4 ：\(\boxed{256}\) is the summation of the binomial coefficients for n=8 and i ranging from 0 to 8

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