(Find the co-efficient of x6 in the expansion of (1

1.	(Find the co-efficient of x6 in the expansion of (1
Answer» The general term in expansion of (1 - y)^-n tr+1= [n(n+1)(n+2)...(n+r-1)/r!].y^r In the expansion of (1 - 2x)^-5/2, we havetr+1 = [(5/2)(5/2+1).....(5/2+r-1)/r!].(2x)^r = [579...........(3+2r)/2^rr!].2^r.x^r Putting r = 6, we gett7 = [579111315/ 2^6*6!].2^6.x^6 = [15015/16]x^6 Therefore, Coefficient of x^6 in expansion of (1 - 2x)^-5/2 is15015/16

Answer»

The general term in expansion of (1 - y)^-n

tr+1= [n(n+1)(n+2)...(n+r-1)/r!].y^r

In the expansion of (1 - 2x)^-5/2, we havetr+1 = [(5/2)(5/2+1).....(5/2+r-1)/r!].(2x)^r

= [5*7*9...........(3+2r)/2^r*r!].2^r.x^r

Putting r = 6, we gett7 = [5*7*9*11*13*15/ 2^6*6!].2^6.x^6

= [15015/16]x^6

Therefore, Coefficient of x^6 in expansion of (1 - 2x)^-5/2 is15015/16

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