anonymous
  • anonymous
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}
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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amistre64
  • amistre64
i cant make head nor hair of it
myininaya
  • myininaya
So I guess we should replace x with y-1
myininaya
  • myininaya
\[1-(y-1)+(y-1)^2-(y-1)^3+(y-1)^4 \cdots \] we really don't need to right this any further all of them will be larger degree than y^2

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myininaya
  • myininaya
write*
myininaya
  • myininaya
that is how i see it anyways
Zarkon
  • Zarkon
you could look at the Taylor polynomial
amistre64
  • amistre64
doesnt (y-1)^3 expand with a y^2 in it?
amistre64
  • amistre64
y^3, 3y^2, 3y, 1
amistre64
  • amistre64
expanding all those terms would create y^2 s
myininaya
  • myininaya
oh yeah you are right
myininaya
  • myininaya
that wouldn't be efficient lol
myininaya
  • myininaya
so we should look at zarkon's way
amistre64
  • amistre64
well, if its the y^2 coeffs; its the pascal triangle diag then
amistre64
  • amistre64
2,1,0 ^ 1 3 6 ...
amistre64
  • amistre64
assuming myins interp is good :)
amistre64
  • amistre64
..... the L of the pascal .... thats equal to the next ones entry ....
amistre64
  • amistre64
|dw:1327354588092:dw|
Zarkon
  • Zarkon
you want a polly that looks like this \[\sum_{k=0}^{17}a_ky^k\] there \(y=x+1\)
Zarkon
  • Zarkon
*where y=x+1
amistre64
  • amistre64
1 1* 1 1 2* 1 1 3 3* 1 1 4 6 4* 1 1510 (10) 5 1
amistre64
  • amistre64
but i think my idea has + and - signs to deal with still
Zarkon
  • Zarkon
I get 816 as the answer
amistre64
  • amistre64
\[{{18}\choose {3}}=816.too\]
asnaseer
  • asnaseer
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?
Zarkon
  • Zarkon
using the Taylor polly amounts to computing \[\frac{\displaystyle\sum_{k=1}^{17}k(k-1)}{2}\]
anonymous
  • anonymous
@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...
asnaseer
  • asnaseer
thats fine @kwenisha - I was just worried in case the experts above left you dazed. :)

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