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Algebra

Cool goIITian

Joined:	31 Dec 2007
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1 Jan 2008 11:22:11 IST

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334

BINOMIAL PLEASE.....

None

find coefficient of x^n in (1+x + 2x^2 + 3x^3+.............+ nx^n )^2 ?

pleaz solve it fully.......

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Nadeem

Blazing goIITian

Joined: 25 Aug 2007

Posts: 521

1 Jan 2008 12:51:17 IST

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(1+x + 2x² + 3x³+.............+ nxⁿ )(1+x + 2x² + 3x³+.............+ nxⁿ )

the coefficient of x^n is 1*n + 1(n-1) + 2( n-2 ) .....( n-1 )1 +n*1

= 2n + _{[k=1 ]}^[n-1] k(n-k)

= 2n + n_{[k=1 ]}^[n-1] k - _{[k=1 ]}^[n-1] k²
on simplifying it becomes 2n + n(n-1)(n+1)/6

= n( n² + 11) /6

Krishna Gopal Singh

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Joined: 29 Dec 2006

Posts: 5153

1 Jan 2008 15:27:42 IST

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Perfect approach nadeem. Well done

PRIYESHHHHHHHHHH PATEL

Cool goIITian

Joined: 31 Dec 2007

Posts: 35

1 Jan 2008 16:44:11 IST

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thanks............

nadeem

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