If (x^(2)+x+1)/(1-x) = a(0) + a(1)x+a(2)...

If `(x^(2)+x+1)/(1-x) = a_(0) + a_(1)x+a_(2)x^(2)+"…."`, then `sum_(r=1)^(50) a_(r)` equal to

148

146

149

none of these

Text Solution

Verified by Experts

The correct Answer is:

`((x^(2)+x+1)(1-x))/((1-x)^(2)) = (1-x^(3))(1-x)^(-2)`
`= (1-x^(3))(1+2x+3x^(2)+"....")`
Now, `a_(r) = (r+1)-(r-2)=3`
But `a_(1) = 2`
So, `underset(r=1)overset(50)suma_(r) = 2+49xx3=149`

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