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Coefficient of x^(18) in (1+x+2x^2+3x^3+...

Coefficient of `x^(18)` in `(1+x+2x^2+3x^3++18 x^(18))^2` equal to `995` b. `1005` c. `1235` d. none of these

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Coefficient of `x^(18)` in `(1+x+2x^(2)+3x^(3)+…+18x^(18))^(2)`
=Coefficient of `x^(18)` in `(1+x+2x^(2)+3x^(3)+..+18x^(18))xx(1+x+2x^(2)+3x^(3)+..+18x^(18))`
`=1xx18+1xx17+2xx16+..+17xx1+18xx1`
`=36+(1xx17+2xx16+..+17xx1)`
`=36+sum_(r=1)^(17)r(18-r)=36+18sum_(r=1)^(17)r-sum_(r=1)^(17)r^(2)`
`=36+18(17(18))/2-(17(18)(35))/6`
=1005
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