Find the sum of \( n \) terms of the series \( (a+b)+\left(a^{2}+a b+b^{2}\right)+\left(a^{3}+a^...

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Find the sum of \( n \) terms of the series \( (a+b)+\left(a^{2}+a b+b^{2}\right)+\left(a^{3}+a^{2} b+a b^{2}+b^{3}\right)+\ldots \) where \( a \neq 1, b \neq 1 \) and \( a \neq b \).
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