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If (1+px)^(n)=1+8x+24x^(2)+ . . ., then ...

If `(1+px)^(n)=1+8x+24x^(2)+ . . .`, then find `(p-n)/(p+n)`

Text Solution

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We have,
`(1+px)^(n)=1+npx+(n(n-1))/(2!)p^(2)x^(2)+` . . .
`=1+8x+24x^(2)`+ . . .
Comparing the coefficient of like terms, we get
`np=8,(n(n-1))/(2)p^(2)=24`
`impliesnp(np-p)=24xx2`
`implies8=p=6`
`impliesp=2`
`impliesn=4 `
Thus `(p-n)/(p+n)=(2-4)/(2+4)=-(1)/(3)`
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