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If the coefficient of x in the expansion...

If the coefficient of x in the expansion of `prod_(r=1)^(110)(1+rx)` is `lambda(1+10)(1+10+10^(2))`, then the value of ` lambda` is

Text Solution

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`:.sum_(r=1)^(110)(1+rx)=(1+x)(1+2x)(1+3x)"...."(1+110x)`
`=1^(100)+(z+2x+3x+"...."+110x)1^(109)+"....."`
So, coefficient of x in
`sum_(r=1)^(110)(1+rx)=(1+2+3+"......"+110)=(110xx111)/(2)=55xx111=6105`
Now, `lambda(1+10)(1+10+10^(2))=lambda(11)(111)`
`implieslambda(11)(111)=6105 implies lambda=5`.
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