Use the Principle of Mathematical Induction to Find the Equivalent $1 + 2 \cdot 2 + 3 \cdot 2 ^ { 2 } + \ldots + n \cdot 2 ^ { n - 1 }$

question 8

Multiple Choice

Use the principle of mathematical induction to find the equivalent expression for every positive integer n. $1 + 2 \cdot 2 + 3 \cdot 2 ^ { 2 } + \ldots + n \cdot 2 ^ { n - 1 }$

• A) \(1 + ( n - 1 ) 2 ^ { n }\)
• B) \(( n - 1 ) 2 ^ { n }\)
• C) \(9 + ( 5 n - 9 ) 2 ^ { n }\)
• D) \(11 ^ { n } - 1\)
• E) \(( 5 n - 9 ) 2 ^ { n }\)

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