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Find the coefficient of x^(50) in the ex...

Find the coefficient of `x^(50)` in the expansion of `(1+x)^(101)xx(1-x+x^2)^(100)dot`

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`(1+x)^(101)(1-x+x^(2))^(100)`
`= (1+x)[(1+x)^(100) (1-x+x^(2))^(100)]`
`= (1+x)(1-x^(3))^(100)`
`= (1-x^(3))^(100) + x(1-x^(3))^(100)`
`= (1-x^(3))^(100) + x(1-x^(3))^(100)`
Now, coefficient of `x^(50)` in `[(1-x^(3))^(100) + x(1-x^(3))^(100)]`
`=` Coefficient of `x^(50)` in `(1-x^(3))^(100)` + Coefficient of `x^(49)` in `(1-x^(3))^(100)`
`= 0` (as 49 and 50 are not a multiple of 3)
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