Question

Write as a single term from Pascal's Triangle in the form t_nr(1 mark)
t_13,8 + t_13,9

Answer 1

¹³C₈ + ¹³C₉ as a single term from Pascal's Triangle is ¹⁴C₉

What is Pascal's triangle?

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.

What is combination?

Combination is the number of ways r in which n objects can be selected. It is given by ⁿCₓ = n!/x!(n - x)!

How to write a single term from Pascal's Triangle in the form t_nr = t_13,8 + t_13,9.

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:

https://brainly.com/question/3442415

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