¹³C₈ + ¹³C₉ as a single term from Pascal's Triangle is ¹⁴C₉
<h3>
What is Pascal's triangle?</h3>
Pascal's triangle is a triangle written in such a way that it forms the coefficients of a binomial expansion. The coefficients of the terms are gotten through combination.
<h3>What is combination?</h3>
Combination is the number of ways r in which n objects can be selected. It is given by ⁿCₓ = n!/x!(n - x)!
<h3 /><h3>How to write a single term from Pascal's Triangle in the form t_nr = t_13,8 + t_13,9.</h3>
Since we have ¹³C₈ + ¹³C₉ and we want to write it as a single term, we have that
- ¹³C₈ = 13!/8!(13 - 8)! = 13!/8!5! and
- ¹³C₉ = 13!/9!(13 - 9)! = 13!/9!4!
So, ¹³C₈ + ¹³C₉ = 13!/8!5! + 13!/9!4!
= 13!/(8! × 5 × 4!) + 13!/(9 × 8! × 4!)
= 13!/8!4![1/5 + 1/9]
= 13!/8!4! × [(9 + 5)/45]
= 13!/8!4! × 14/45]
= 13!/8!4! × 14/(9 × 5)]
= 14 × 13!/8! × 9 × 4! × 5)]
= 14!/9!5!
= 14!/9!(14 - 9)!
= ¹⁴C₉
So, ¹³C₈ + ¹³C₉ as a single term from Pascal's Triangle is ¹⁴C₉
Learn more about Pascal's triangle here:
brainly.com/question/3442415
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