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Math Challenge lll Winter 2023-2024 Combinatorics

 
 
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Math Challenge lll Winter 2023-2024 Combinatorics
by Bella Xiao - Friday, December 22, 2023, 7:50 AM
 

Hi! I am having  trouble on problem 3.3 3.6 and 3.8

For problem 3.8, I already know that a3=1+C(4,1) +C(5,2)+ C(6,3)+...+C(47,50) but I don't know what to do next

Help would be appreciated.

 
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Re: Math Challenge lll Winter 2023-2024 Combinatorics
by John Lensmire - Friday, December 22, 2023, 11:14 AM
 

You're very close! Here's a quick hint: your sum can be expressed as C(3,3) + C(4,3) + C(5,3) + C(6,3) + ....

Is there an identity that can help from here?