Prove the following generalization of the De Morgan’s law using induction (Aj ⊆U;j=1,...,n)
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Prove the following by using the principle of mathematical induction for all $n \in \mathbf{N}$. $$ a+a r+a r^{2}+\ldots+a r^{n-1}=\frac{a\left(r^{n}-1\right)}{r-1} . $$
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