
Binomial questions 2
Hi I've some more questions, your help is greatly appreciated!
1.) $\displaystyle (x^23x+1)^2=x^4gx^3+11x^26x+1$ and the sum of it's coefficients is 1, what is the sum of the coefficients of
$\displaystyle (x^3+2x^2+3x7)^{100}?$
I really have no idea how to start, can't see any patterns..
2a.) Prove that $\displaystyle r{n \choose r}=n{n1 \choose r1} $
I did this ok so ignore this part! I had just typed it down as this part may yield a clue for the other parts.
2b.) Hence show that $\displaystyle {n \choose 1}+2{n \choose 2}+3{n \choose 3}+4{n \choose 4}+...+n{n \choose n}=n2^{n1}$
2c.) Suppose the numbers Pr ( r is a subscript!) are defined by
$\displaystyle Pr={n \choose r} p^r(1p)^{nr} for r=0,1,2,3...,n.$
Prove that
$\displaystyle \sum\limits_{r=0}^nPr=1$
and that
$\displaystyle \sum\limits_{r=1}^nrPr=np$
How do I do them! Please help me thank you so much!!!

Re: Binomial questions 2
Sorry for question 1, it is not $\displaystyle gx^3$ but $\displaystyle 6x^3$, sorry for the typo and thank you!