Let (T(n)=sum_{k=0}^{n}(-1)^{k}left(begin{array}{l}n kend{array}ight)). (a) Use Pascal's Triangle to compute (T(n)) for (n=1,2,3,4). (b) Prove that (T(n)=0)
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Let \(T(n)=\sum_{k=0}^{n}(-1)^{k}\left(\begin{array}{l}n \\ k\end{array}ight)\).
(a) Use Pascal's Triangle to compute \(T(n)\) for \(n=1,2,3,4\).
(b) Prove that \(T(n)=0\) for all \(n \geq 1\). Expand \((a+b)^{n}\) and evaluate at \(a=1, b=-1\).
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I'm Ali Arif from Islamabad Pakistan. I have completed my MBA with a specialization in supply chain Management from SZABIST Islamabad in 2019 and my Bachelor’s degree (BBA) from FAST-NU, Islamabad in 2015. Currently, I’m working at ZONES UK LTD as a Buyer EMEA. In addition, I’m also currently doing CIPS Level 5 (chartered institute in procurement and supply operations).
In my university, I happened to review several business plans in NESCOM Event at FAST while serving as a panel judge. During my education, I have served as a Teacher's Assistant for many professors for varied subjects and had an opportunity to teach students of different semesters and departments. As a Voluntary Teaching Assistant, I have taught fresh to final year students formulating activities, lessons, and helped the instructor to execute them.
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