(See Steps) Prove each of the statements in 35-40, assuming n is an integer variable that takes positive integer values. Use identities from Section $4.2$ as
Question: Prove each of the statements in \(35-40\), assuming \(n\) is an integer variable that takes positive integer values. Use identities from Section $4.2$ as needed.
\(2+2 \cdot 3^{2}+2 \cdot 3^{4}+\cdots+2 \cdot 3^{2 n}\) is \(\Theta\left(3^{2 n}\right)\)
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