Question

help me in this problem

Answer 1

Find out in terms of n
\[\sum_{r=1}^{n}r ^{2}* nCr\]

Answer 2

we have to find a closed form right ?

Answer 3

yeah

Answer 4

hm $$\large 2^{n-2} \times n \times (n+1)$$

Answer 5

how??

Answer 6

You can verify by induction .. I guessed it by chekcing up few terms .. ;)

Answer 7

i guess the answer is somewhat different..

Answer 8

what is the answer ?

Answer 9

wait a while

Answer 10

hmmm.. right u r
but i wanna know the exact process..

Answer 11

ok, i solved it myself right now... thanx a lot, @ foolformath :)

Answer 12

You are welcome, how you solve it ?

Answer 13

n^2=n(n-1)+n

Answer 14

what is that ?

Answer 15

it will help u to get the expression. anyway, bye for now.. will post the solution later..

Answer 16

duh ...

Answer 17

howz that help you ?

Answer 18

you derived the closed form based on that ?

Answer 19

yeah

Answer 20

u can also do it by differenciating

Answer 21

but dont worry, i will be back and will post the solution..

Answer 22

Sure, When you do just post the one you did with using $$ n^2=n(n-1)+n$$ and the derivative one is pretty obvious, expand (1+x)^n then do derivative with respect to x after that multiply with x and then again do the derivative you will left with with something like this $$ (-1+n) n x (1+x)^{-2+n}+n (1+x)^{-1+n}$$ in the LHS and subsitute x =1 you will have your required closed form in both RHS and LHS.