• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Trying to prove this equality involving a summation of a binomial coefficient.

  • Thread starter jdinatale
  • Start date
I immediately thought of induction, so that is what I used, but I can't seem to make any progress past a certain point.

1-1.png


2-1.png
 

tiny-tim

Science Advisor
Homework Helper
25,790
242
hi jdinatale! :smile:

(i haven't looked at your induction proof , but …)

why not just multiply the LHS by n+1 ? :wink:
 
hi jdinatale! :smile:

(i haven't looked at your induction proof , but …)

why not just multiply the LHS by n+1 ? :wink:
Ok, I tried that and I eventually could not go any further. Any ideas on what's going wrong?

3-1.png
 

tiny-tim

Science Advisor
Homework Helper
25,790
242
hi jdinatale! :smile:

in the third line you have ∑k=0…j j+1Ck+1

put m = k+1, that's ∑m=1…j+1 j+1Cm

what is that? :wink:
 
hi jdinatale! :smile:

in the third line you have ∑k=0…j j+1Ck+1

put m = k+1, that's ∑m=1…j+1 j+1Cm

what is that? :wink:
Brilliant! I've solved the problem now, thank you so much. But please tell me, how did you possibly know to do that? That was not obvious to me at all, and I'm not sure how you would just know to do that.
 

tiny-tim

Science Advisor
Homework Helper
25,790
242
easy! :smile:

the clue was in the question …

the RHS said 2n+1,

which i know is ∑ n+1Cr :wink:
 

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top