Sign up for your FREE 7-day trial.Get instant access to all the benefits of SparkNotes PLUS! Cancel within the first 7 days and you won't be charged. We'll even send you a reminder.
SparkNotes Plus subscription is $4.99/month or $24.99/year as selected above. The free trial period is the first 7 days of your subscription. TO CANCEL YOUR SUBSCRIPTION AND AVOID BEING CHARGED, YOU MUST CANCEL BEFORE THE END OF THE FREE TRIAL PERIOD. You may cancel your subscription on your Subscription and Billing page or contact Customer Support at custserv@bn.com. Your subscription will continue automatically once the free trial period is over. Free trial is available to new customers only.
Step 2 of 4
Choose Your Plan
Step 3 of 4
Add Your Payment Details
Step 4 of 4
Payment Summary
Your Free Trial Starts Now!
For the next 7 days, you'll have access to awesome PLUS stuff like AP English test prep, No Fear Shakespeare translations and audio, a note-taking tool, personalized dashboard, & much more!
Thanks for creating a SparkNotes account! Continue to start your free trial.
Please wait while we process your payment
Your PLUS subscription has expired
We’d love to have you back! Renew your subscription to regain access to all of our exclusive, ad-free study tools.
Did you know you can highlight text to take a note?x
Pascal's Triangle
Pascal's Triangle is a triangle in which each row has one more entry than
the preceding row, each row begins and ends with "1," and the interior elements
are found by adding the adjacent elements in the preceding row. The triangle is
symmetrical.
Figure %: Pascal's Triangle
In Row 6, for example, 15 is the sum of 5 and 10, and 20 is the sum of 10 and
10. Note that the triangle begins with Row 0.
We can find any element of any row using the combination function. The rth element
of Row n is given by:
C(n, r - 1) =
For example, the 3rd entry in Row 6 (r = 3, n = 6) is
C(6, 3 - 1) = C(6, 2) = = 15.
Examples
What is the 5th entry in the Row 7 of Pascal's Triangle? C(7, 4) = = 35.
What is the 6th entry in Row 5 of Pascal's Triangle? C(5, 5) = = 1
What is the 9th entry in Row 20 of Pascal's Triangle? C(20, 8) = = 125970
What is the 2nd entry in Row 103 of Pascal's Triangle? C(103, 1) = = 103
= 15
= 35
= 1
= 125970
= 103
