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February 27th, 2019, 01:04 PM  #1 
Newbie Joined: Dec 2017 From: usa Posts: 4 Thanks: 0  help with newton binum
hello everyone, I have a few questions about newton's binum. I was requested to calculates the following: http://www.interload.co.il/upload/9048222.png I have no clue how to calculte either of them our teacher doesn't explained it I will be very glad if someone could help me with them and show me the way of solution thank you 
February 28th, 2019, 10:05 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,373 Thanks: 1276 
$(a+b)^n = \sum \limits_{k=0}^n \dbinom{n}{k} a^k b^{nk}$ $\text{Let }b=1$ and see what that gets you. For the second one note that by the nature of Pascal's triangle $\dbinom{n+1}{k} = \dbinom{n}{k1}+\dbinom{n}{k}$ Write out some of the sum until you see the pattern and simplify it to obtain the term on the right hand side. 
February 28th, 2019, 11:43 AM  #3 
Newbie Joined: Dec 2017 From: usa Posts: 4 Thanks: 0 
Hey firstly thanks for the rapid answer I miss understood you about the second one I been told that I need to solve it by combinatorics by inventing a problem and solve with it both sides of the euquation; also about the first one when you say comaring b to 1 how should I do it cause I have no idea how to solve that thanks 
February 28th, 2019, 12:11 PM  #4  
Senior Member Joined: Sep 2015 From: USA Posts: 2,373 Thanks: 1276  Quote:
Then you get $a^n = \sum \limits_{k=1}^n \dbinom{n}{k}a^k$ like for example $5^n = \sum \limits_{k=0}^n 5^k \dbinom{n}{k}$ Does that term on the right look familiar?  

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