Binomial (1 Viewer)

[Hello_World2]

Can anyone help with these 4 questions, I tried expanding and simplifiying the questions but I still couldn't find the answer. Help is appreciated, thnaks!

 

[Lith_30]

Think of the pascal triangle and lets see if we can develop some patterns, as the pascal triangle can be developed through the combinations.


as we can see, each of the numbers in the pascal triangle can be generated by adding the two numbers closest to it in the row above.

ie , , ,

Which can also be represented in this form , , ,

from this we can see that a pattern forms where the general term would be

using this identity the questions shouldn't be to hard now

 

[Hello_World2]

Think of the pascal triangle and lets see if we can develop some patterns, as the pascal triangle can be developed through the combinations.
View attachment 36599

as we can see, each of the numbers in the pascal triangle can be generated by adding the two numbers closest to it in the row above.

ie , , ,

Which can also be represented in this form , , ,

from this we can see that a pattern forms where the general term would be

using this identity the questions shouldn't be to hard now

I see, thanks a lot !