Question

The polynomial 1-x+x ^{2}-x ^{3}+...-x ^{15}+x ^{16}-x ^{17} can be written as a polynomial in y=x+1. Find the coefficient of y ^{2}

Answer 1

i cant make head nor hair of it

Answer 2

So I guess we should replace x with y-1

Answer 3

\[1-(y-1)+(y-1)^2-(y-1)^3+(y-1)^4 \cdots \]
we really don't need to right this any further all of them will be larger degree than y^2

Answer 4

write*

Answer 5

that is how i see it anyways

Answer 6

you could look at the Taylor polynomial

Answer 7

doesnt (y-1)^3 expand with a y^2 in it?

Answer 8

y^3, 3y^2, 3y, 1

Answer 9

expanding all those terms would create y^2 s

Answer 10

oh yeah you are right

Answer 11

that wouldn't be efficient lol

Answer 12

so we should look at zarkon's way

Answer 13

well, if its the y^2 coeffs; its the pascal triangle diag then

Answer 14

2,1,0
^

1
3
6
...

Answer 15

assuming myins interp is good :)

Answer 16

..... the L of the pascal .... thats equal to the next ones entry ....

Answer 17

you want a polly that looks like this

\[\sum_{k=0}^{17}a_ky^k\]


there \(y=x+1\)

Answer 18

*where y=x+1

Answer 19

1
1* 1
1 2* 1
1 3 3* 1
1 4 6 4* 1
1510 (10) 5 1

Answer 20

but i think my idea has + and - signs to deal with still

Answer 21

I get 816 as the answer

Answer 22

\[{{18}\choose {3}}=816.too\]

Answer 23

I notice that the person you guys are trying to assist has not said a word yet.
@kwenisha - does all this make any sense to you? have you attempted it yourself using a different method? any thoughts?

Answer 24

using the Taylor polly amounts to computing

\[\frac{\displaystyle\sum_{k=1}^{17}k(k-1)}{2}\]

Answer 25

@Asnaseer, I am actually trying understand it while working with my partner... I apologize if I come off as just trying to get the answer and not trying to understand it...

Answer 26

thats fine @kwenisha - I was just worried in case the experts above left you dazed. :)