Question

please help - binomial thm
http://prntscr.com/3ib7w4

Answer 1

\[(a+b)^n = \sum \limits_{k=0}^n \binom{n}{k}a^{n-k}b^k\]

Answer 2

so ur qn , prove ?

Answer 3

yeah prove the given statement

Answer 4

using the given hint, do i get :

\[n(a+b)^{n-1} = n\sum \limits_{k=0}^{n-1} \binom{n-1}{k} a^{n-1-k}b^k\]

?

Answer 5

letting a = 1 :

\[n(1+b)^{n-1} = n\sum \limits_{k=0}^{n-1} \binom{n-1}{k}b^k \]

Answer 6

not sure how to mess wid that \(n\) before summation

Answer 7

well, ur second statment is directly apply binomial theorm right , hmm

Answer 8

whichh statement ?

Answer 9

\[n(1+b)^{n-1} = \sum \limits_{k=0}^{n-1} n\binom{n-1}{k}b^k = \sum \limits_{k=0}^{n-1} (k+1)\binom{n}{k+1}b^k \]

Answer 10

used the second hint given

Answer 11

why n inside the sum ??
its out of it i guess

Answer 12

yes, but it should not matter as the variable is "k", right ?

Answer 13

oki i got ur point
so prove that