Can anybody here help me with this simple problem? I've been thinking about this for half an hour and I am not able to come to a solution.
How does $3^n-1+2 \cdot 3^n$ evaluate to $3^{n+1}-1$?
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3 Answers
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Note that $$3^{n+1} = 3 \cdot 3^n = (1+2)3^n = 3^n+2\cdot 3^n$$
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$3^n -1 + 2\cdot3^n$ = $3\cdot3^n -1$
= $3^{n+1}-1 $
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Hint: $(1+2)3^n-1 \implies 3^{n-1}-1$. Grouping terms.
