Question

Evaluate the sum of series from (k=o to 5 ) (-1)^k combination of (5
k)

Answer 1

\[\sum_{k=0}^{3} \left(\begin{matrix}3 \\ k\end{matrix}\right) (-1)^{k}\] Evaluate this using binomial thorem please. \[\sum_{k=0}^{n} \left(\begin{matrix}n \\ k\end{matrix}\right) a ^{n-k}b ^{k}\]

Answer 2

Since the last sum is equivalent to \((a+b)^n\), you can simply set \(a=1\) and \(b=-1\), with \(n=3\). What's \(1-1\)?