Question
$$\text { Show that: }\left(\begin{array}{c}k \\0\end{array}\right)=\left(\begin{array}{c}k+1 \\0\end{array}\right)$$
Step 1
Step 1: We know that the binomial coefficient is defined as: $$\left(\begin{array}{c}n \\k\end{array}\right) = \frac{n!}{k!(n-k)!}$$ where $n!$ denotes the factorial of $n$, which is the product of all positive integers up to $n$. Show more…
Show all steps
Your feedback will help us improve your experience
Linh Vu and 97 other Precalculus educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
$$\text { Show that: }\left(\begin{array}{l}k \\k\end{array}\right)=\left(\begin{array}{l}k+1 \\k+1\end{array}\right)$$
Sequences, Induction, and Probability
The Binomial Formula
$$\text { Show that: }\left(\begin{array}{c}k \\r-1\end{array}\right)+\left(\begin{array}{c}k\\r\end{array}\right)=\left(\begin{array}{c}k+1 \\r\end{array}\right)$$
Prove that $\left(\begin{array}{c}n+1 \\ k\end{array}\right)=\left(\begin{array}{l}n \\ k\end{array}\right)+\left(\begin{array}{c}n \\ k-1\end{array}\right).$
Probability
Tools for Counting Sample Points
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD