Question

Question on binomial theorem

Answer 1

\[\sum_{r=0}^{n}r ^{2} C _{r}^{2}\]

Answer 2

@UnkleRhaukus

Answer 3

HI!!

Answer 4

how are you interpreting \(\binom{2}{r}\) for \(r>2\)? usually that is zero

Answer 5

in which case this is only
\[1^2+2^2=5\]

Answer 6

I don't get you. Plus that 2 on the top means square, if that's what you are asking.

Answer 7

oh ok then what does \(C_2\) mean?

Answer 8

sorry i meant \(C_r\)
what is being squared?

Answer 9

\[C _{r}\] is being squared

Answer 10

ok let me ask it this way
what is \(C_3\) ?

Answer 11

that's clearly 2 choose r
\[C_{r}^{2}\]

Answer 12

@xapproachesinfinity apparently it is not (according to @pratyush5 )

Answer 13

Wait, I am gonna write the question another way.

Answer 14

that's not squared?

Answer 15

are you sure!?

Answer 16

\(C_r\) is not defined yet, if it is some quantity to be squared
if it is \(C_r^2=\binom{2}{r}\) then it is zero if \(r>2\)

Answer 17

\[1^{2.}C _{1}^{2} + 2^{2}.C _{2}^{2} + 3^{2}.C _{3}^{2} ......\] and so on

Answer 18

if so you will have something of this form C1 C2 C3 C4 with the square remaining on top

Answer 19

@xapproachesinfinity Thats what I have.

Answer 20

ok then it is 5