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asked 2021-09-03
Provided a function that would be defined fo every natural number n as: \[g(n)=\frac{2}{2}+\frac{1}{4}+\frac{1}{8}+\cdot\cdot\cdot+\frac{1}{2^{n-1}}+\frac{1}{2^{n}}\] COnjecture a closed form form for g(n) (a simple expression devoid of signs or dots) while also using mathematical induction to prove that the conjecture is true.
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